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What is the base of a triangle if the area is equal to 420 square inches and the height is 5 times the base less 10 inches?
SMILESMtgy
Let the height be (5x-10) and the base be x:
1/2*(5x-10)*x = 420 square inches
Multiply both sides by 2 and multiply out the brackets:
5x2-10x = 840
5x2-10x-840 = 0
Solving the above quadratic equation works out as:
x = -12 or x = 14 it must be the latter because dimensions can't be negative.
Therefore: base = 14 inches and height = 60 inches
Check: 1/2*14*60 = 420 square inches
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What is the area of an equilateral triangle with sides 10 inches and height of 7 inches?
Area of the equilateral triangle: 0.5*10*10*sin(60 degrees) = 25 times square root of 3 which is about 43.301 square inches to 3 decimal places. If it is an equilateral triangle with 3 equal sides of 10 inches then its height would be about 8.66 inches and not 7 inches
Can you work out the area of an equilateral triangle with a perimeter of XXVII inches giving details of your work?
XXVII = 27 An equilateral triangle with a perimeter of 27 inches has three equal sides of 9 inches. Area of a triangle = base times its perpendicular height divided by 2. An equilateral triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can find its height by using Pythagoras' Theorem: hypotenuse2 - base2 = height2 92-4.52 = 60.75 square inches. Square root of 60.75 = 7.794228634 inches. Area = 9x7.794228634/2 = 35.07402885 square inches. Therefore area of an equilateral triangle with a perimeter of 27 inches is 35.074 square inches correct to 3 decimal places. Answered by David Gambell, Merseyside, England.
How do you work out the area of an equilateral triangle with a perpendicular height of XV inches showing details of your work and giving your final answer to an appropriate degree of accuracy?
Height in inches = XV=15 Area of a triangle = base length times perpendicular height divided by 2 An equilateral triangle has three equal sides with three equal interior angles of 60o An equilateral triangle can be considered as being two right angled triangles joined together. So we can make use of trigonometry to find the base length: opposite/tangent = adjacent length of the right angled triangle 15/tangent 60o = 8.660254038 inches Base length of the equilateral triangle = 8.660254038*2 = 17.32050808 inches Area = 17.32050808*15/2 = 129.9038106 square inches Therefore the area of the equilateral triangle is 130 square inches which is correct to three significant figures. Answered by David Gambell, Merseyside, England.
Can you find the dimensions of an isosceles triangle with an area of XII square inches and a height of IV inches showing details of your work?
First find the length of the base: base = area times 2 divided by height base = 12x2/4 = 6 inches An isosceles triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can use Pythagoras' Theorem to find the hypotenuse: base2+height2 = hypotenuse2 32+42 = 25 square inches. Square root of 25 = 5 inches Therefore the isosceles triangle has two equal sides of V inches and a base of VI inches.
An equilateral triangle and a square have equal perimeters what is the ratio of the area of the triangle to the area of the square?
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.
A square and a triangle have equal areas and a side of the square is 10 inches and the base of the triangle is 10 inches then what is the height of the triangle?
Area triangle = 1/2 base x height Area square = length x width = 10in x 10in = 100sq in. Area triangle = area square Therefore: 1/2 x 10in x height = 100sq in height = 100 sq in x 2 / 10 in = 20 in
What is the area of an equilateral triangle with side of 10 inches and height of 7 inches?
Area of the equilateral triangle: 0.5*10*10*sin(60 degrees) = 25 Times Square root of 3 which is about 43.301 square inches to 3 decimal places. If it is an equilateral triangle with 3 equal sides of 10 inches then its height would be about 8.66 inches and not 7 inches
What is the area of an equilateral triangle with sides 10 inches and height of 7 inches?
Area of the equilateral triangle: 0.5*10*10*sin(60 degrees) = 25 times square root of 3 which is about 43.301 square inches to 3 decimal places. If it is an equilateral triangle with 3 equal sides of 10 inches then its height would be about 8.66 inches and not 7 inches
How can you find the base of a right triangle when you have the height and hypotenuse?
The square of the length of the base plus the square of the length of the height will equal the square of the length of the hypotenuse of your right triangle, per Pythagoras. Square the hypotenuse, subtract the square of the height, and then find the positive square root of that and you'll have the base of your right triangle.
A rectangle and triangle have equal areas - the rectangle's length is 12 inches and its width is 8 inches so if the base of the triangle is 32 inches what is the length in inches of the altitude drawn?
The rectangle has an area of 12 x 8 = 96 square inches. The triangle has an area of (1/2 * 32 * x). So, 16x = 96, therefore x = 6. The height of the triangle is 6 inches.
If a square and a triangle have an area of sixty four square centimeters if the length of the triangle is the same as the length of a side of the square what is the height of the triangle?
You do not indicate if the given area is the total area of the square and the triangle. Or whether they are equal values.
Can you work out the area of an equilateral triangle with a perimeter of XXVII inches giving details of your work?
XXVII = 27 An equilateral triangle with a perimeter of 27 inches has three equal sides of 9 inches. Area of a triangle = base times its perpendicular height divided by 2. An equilateral triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can find its height by using Pythagoras' Theorem: hypotenuse2 - base2 = height2 92-4.52 = 60.75 square inches. Square root of 60.75 = 7.794228634 inches. Area = 9x7.794228634/2 = 35.07402885 square inches. Therefore area of an equilateral triangle with a perimeter of 27 inches is 35.074 square inches correct to 3 decimal places. Answered by David Gambell, Merseyside, England.
A rectangle and triangle have equal areas The rectangle is 12 inches long and 8 inches wide If the base of the triangle is 32 inches what is the length in inches of the altitude drawn to the base?
Area Rectangle = 12 * 8 = 96 sq. in.Area Triangle = 1/2 base * height -> 96 = 16 * height -> 96 / 16 = height = 6 in.
Why is base times height divided by 2?
Because they derive the formula from the area of a square. A square is width x height (or base x height). If you cut the square into two equal triangles, you can get the area of only a single triangle by dividing by 2.
What are the equal sides of a right angle isosceles triangle when its area is 32 square inches?
The two equal sides each measure 8 inches
How do you work out the area of an equilateral triangle with a perpendicular height of XV inches showing details of your work and giving your final answer to an appropriate degree of accuracy?
Height in inches = XV=15 Area of a triangle = base length times perpendicular height divided by 2 An equilateral triangle has three equal sides with three equal interior angles of 60o An equilateral triangle can be considered as being two right angled triangles joined together. So we can make use of trigonometry to find the base length: opposite/tangent = adjacent length of the right angled triangle 15/tangent 60o = 8.660254038 inches Base length of the equilateral triangle = 8.660254038*2 = 17.32050808 inches Area = 17.32050808*15/2 = 129.9038106 square inches Therefore the area of the equilateral triangle is 130 square inches which is correct to three significant figures. Answered by David Gambell, Merseyside, England.
Can you find the dimensions of an isosceles triangle with an area of XII square inches and a height of IV inches showing details of your work?
First find the length of the base: base = area times 2 divided by height base = 12x2/4 = 6 inches An isosceles triangle can be considered as being two right angled triangles joined together. So by halving the length of the base we can use Pythagoras' Theorem to find the hypotenuse: base2+height2 = hypotenuse2 32+42 = 25 square inches. Square root of 25 = 5 inches Therefore the isosceles triangle has two equal sides of V inches and a base of VI inches.
