First find its height by dividing its area and use Pythagoras to find its sides:
Height: 84.9072/(0.5*15.96) = 10.64 cm
Half its base: 7.98 cm
Pythagoras: 10.64 squared plus 7.98 squared = 176.89 and its sq rt = 13.3
Perimeter therefore is: 2*(13.3)+15.96 = 42.56 cm
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
Three triangles are: scalene, which has three sides of different lengths, isosceles, which has two sides with the same length, and equilateral, which has three sides that are all the same length. In the picture, the scalene triangle is triangle RST, the isosceles triangle is triangle XYZ, and the equilateral triangle is triangle ABC. If two sides or more sides of a triangle have a little line on them, then they are the same length. Click on the related link, "Three Triangles", to see them.
21.2268 = 0.5 x base x 5.32 base = (21.2268)/(0.5 x 5.32) = (21.2268/2.66) = 7.98 Half the base = 3.99 Now one of the equal sides of the isosceles triangle (using pythagoras theorem) is sqrt(3.99^2 + 5.32^2) = sqrt(15.92 + 28.30) = sqrt(44.22) = 6.65 Therefore perimeter of triangle is = base + 2x6.65 = 7.98 + 13.3 = 21.28 cm
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.
Let the sides be s:- If: 0.5*s squared*sin(60 degrees) = 97.428 Then: s = square root of 97.428*2/sin(60 degrees) => 15.00001094 Perimeter: 3*15 = 45 cm
These are basically the steps: * Use the formula for the area of a triangle to calculate the height. * Use the height and half the base to calculate the lateral sides. Use the Pythagorean Theorem. (It helps to draw a sketch, to visualize the situation.) * Add the three sides to get the perimeter.
Three triangles are: scalene, which has three sides of different lengths, isosceles, which has two sides with the same length, and equilateral, which has three sides that are all the same length. In the picture, the scalene triangle is triangle RST, the isosceles triangle is triangle XYZ, and the equilateral triangle is triangle ABC. If two sides or more sides of a triangle have a little line on them, then they are the same length. Click on the related link, "Three Triangles", to see them.
21.2268 = 0.5 x base x 5.32 base = (21.2268)/(0.5 x 5.32) = (21.2268/2.66) = 7.98 Half the base = 3.99 Now one of the equal sides of the isosceles triangle (using pythagoras theorem) is sqrt(3.99^2 + 5.32^2) = sqrt(15.92 + 28.30) = sqrt(44.22) = 6.65 Therefore perimeter of triangle is = base + 2x6.65 = 7.98 + 13.3 = 21.28 cm
Area: 0.5*9.96*height = 33.0672 sq cmHeight: (33.0672*2)/9.96 = 6.64 cmAn isosceles triangle is in effect two right angle triangles joined together at its line of symmetry and in this case have bases of 9.96/2 = 4.98So using Pythagoras: 6.64 squared+4.98 squared = 68.89Square root of 68.89 = 8.3 which is its hypotenusePerimeter therefore is: 8.3+8.3+9.96 = 26.56 cmBase angles: tangent^-1(6.64/4.98) = 53 degrees to nearest degree
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.
Let the sides be s:- If: 0.5*s squared*sin(60 degrees) = 97.428 Then: s = square root of 97.428*2/sin(60 degrees) => 15.00001094 Perimeter: 3*15 = 45 cm
Formula: 0.5*a*b*sinC = area or 0.5*side2*sinC = area Apex angle: 180-75-75 = 30 degrees So: 0.5*side2*sin30 = 100 square cm Side as subject of the formula: side = square root of (200/sin30) = 20 Therefore: each equal sides of the isosceles triangle are 20 cm in length
Area: 0.5*8.75*8.75*sin(54 degrees) = 31.0 square cm to 3 significant figures
Suppose the base of the triangle is of length x cm and the equal sides are of length y cm.The base angles sum to 60 degrees so each is 30 degrees and the apex angle is 180-60 = 120 degrees.Then area = 132.61014 = 0.5*y2*sin(120)So that y2 = 132.61014/[0.5*sin(120)] = 306.25and therefore, y = 17.5 cm.Then, by the sine rule, x/sin(120) = y/sin(30)So x = y*sin(120)/sin(30) = 30.31 cmAnd therefore, perimeter = x + 2*y = 65.31 cm.
Let the number be x and so: 2x squared+3x = 77.2502 Then: 2x squared+3x-77.2502 = 0 Solving the above quadratic equation gives x a positive value of 5.51 Thus: congruent sides are each 30.3601 cm and base is 16.53 cm Check: 30,3601+30.3601+16.53 = 77.2502 cm
it should be a triangle with no red showing
Here are the key aspects of work; I'll leave the details of the calculation to you. 1) Write an equation for the area, in terms of variables "w" and "h" (for width and height). 2) Write an equation for the length of the diagonal, in terms of "w" and "h". (Hint: Use the Pythagorean Theorem.) 3) Solve the two equations. 4) Calculate the perimeter, based on length and width.