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Is the product of the lengths of the legs of a right triangle equal to the product of the lengths of the hypotenuse and the altitude?
Wiki User
∙ 14y ago
No. I have two ways to disprove that hypothesis in a hurry.
1). The right triangle can be set down on either leg, so either leg can be the altitude.
That would give you two different possibilities for the product of (hypotenuse x altitude),
and they couldn't both be equal to the same number.
2). If I can find one counter-example, that blows it right there.
Take the simple, 3-4-5 right triangle.
The product of the legs is (3 x 4) = 12.
The product of the (hyp x alt) is either (5 x 3) = 15 or (5 x 4) = 20. Neither one is 12.
The hypothesis is demolished. It is dead meat.
Wiki User
∙ 14y ago
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How do you find the base and height of a triangle when you only have the area of the triangle?
If you only have the triangle's area, then you only know the product of (base times height) ... it's double the area ... but you can't tell what either of those individual lengths is.
How many possible right triangles have an area of 20 units squared?
An infinite number. All you need is any right triangle where the product of the lengths of the two legs is 40.
What is the area of a triangle with a hypotenuse of 17 and height of 15?
The reference to hypotenuse tells you that this is a right triangle, so the Pythagorean theorem applies. You can't figure area until you know both legs of the right triangle. Letting x be unknown side, you can write 15^2 + x^2 = 17^2. Rearranging: x^2 = 17^2 - 15^2. Use a calculator. x turns out to be a whole number. The area of a right triangle is half the product of its sides (picture a rectangle cut in half diagonally). That would be (x*15)/2.
If each side of the equilateral triangle measures 9c find the height of the triangle?
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
The area of a rhombus equals two times the product of the lengths of its diagonals?
false
What is the hypotenuse of a 12 foot by 12 foot triangle?
To find the hypotenuse, add 12 squared plus 12 squared. Then take the square root of that product which is 16.9705627.
How do you find the area of a triangle with side lengths?
If you are only given the side lengths of a scalene triangle, it is impossible for you to find for the area, unless you are given more information... like the height of the triangle for example. If this is a right triangle you would like to find the area of, you can multiply the length of each leg with each other, and then divide that product by 2 to conclude the area of the triangle.
The area formula for a trapezoid?
The area of a trapezoid is one-half the product of the length of an altitude and the sum of the lengths of the bases: A=1/2(b1 + b2)
How do you find the base and height of a triangle when you only have the area of the triangle?
If you only have the triangle's area, then you only know the product of (base times height) ... it's double the area ... but you can't tell what either of those individual lengths is.
What is the length of the base of a triangle with the height of 9 meters and area of 18 meters?
Since the area is equal to 1/2 of the product of base and altitude, the base of this triangle must be 4 meters.
What is the area of a triangle that is 12 in and 16 in?
What is 12 in ? And what is 16 in ? ? Are they the lengths of two sides of the triangle ? Are they the length of one side and the height of the triangle ? The area of any triangle is 1/2 of the product of (length of its base) x (its height).
What is the area of a right triangle with side lengths of 6 and 13?
half of the product of these two sides ie (6 x 13)/2 ie 39
How many possible right triangles have an area of 20 units squared?
An infinite number. All you need is any right triangle where the product of the lengths of the two legs is 40.
How do you find the length of one side of a rectangle if the area is 57cm2 and one length is 6cm?
The are of a rectangle is equal to the product of the lengths of its base and altitude. Since its area is 57cm^2, it seems that the altitude is 6 cm. So, A = bh 57 = 6b b = 57/6 b = 9.5 cm
What is the area of a triangle with a hypotenuse of 17 and height of 15?
The reference to hypotenuse tells you that this is a right triangle, so the Pythagorean theorem applies. You can't figure area until you know both legs of the right triangle. Letting x be unknown side, you can write 15^2 + x^2 = 17^2. Rearranging: x^2 = 17^2 - 15^2. Use a calculator. x turns out to be a whole number. The area of a right triangle is half the product of its sides (picture a rectangle cut in half diagonally). That would be (x*15)/2.
Formula of area and perimeter of a hexagon?
for perimeter add up the lengths of the six sides and for area divide the hexagon into six equilateral triangle, find the area of one, and multiply the product by six
If each side of the equilateral triangle measures 9c find the height of the triangle?
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
