Since the two figures are similar, their areas are proportional to the square of their corresponding side lengths.
Let x be the length of the corresponding side in the smaller triangle.
Therefore, the area of the smaller triangle can be calculated as follows:
Area of larger triangle / Area of smaller triangle = (side length of larger triangle / side length of smaller triangle)^2
135 / Area of smaller triangle = (8 / x)^2
Area of smaller triangle = x^2 = 135 * x^2 / 64
x^2 = 135 * x^2 / 64
64 = 135
64x^2 = 135x^2
64x^2 - 135x^2 = 0
-71x^2 = 0
x^2 = 64/71
x ≈ 0.899
Therefore, the area of the smaller triangle, to the nearest whole number, is 0.899 ft²
The pair of figures to the right are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number.
Area of larger triangle = 135 ft²
1 answer