SOLUTION: Prove that the ratio of the areas of two similer triangles is equal to the squares of the ratio of their corresponding sides

Question 1006494: Prove that the ratio of the areas of two similer triangles is equal to the squares of the ratio of their corresponding sides
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
if the triangles are similar, then all corresponding parts are proportional which means the ratios of the corresponding parts are the same.

the altitude of a triangle counts as a corresponding part.

let the area of triangle 1 be 2/3 * b * h
b is the base
h is the height.

let the area of triangle 2 be 2/3 * xb * xh

x is the common ratio.

A1 = area of triangle 1 = 1/2 * b * h

A2 = area of triangle 2 = 1/2 * xb * xh

the ratio of the area of A2 to the area of A1 is (1/2 * xb * xh) / (1/2 * b * h)

since xb * xh is the same as x^2 * b * h, the ratio of A2 to A1 becomes:

A2 / A1 = (1/2 * x^2 * b * h) / (1/2 * b * h)

the (1/2 * b * h) in the numerator cancels out with the (1/2 * b * h) in the denominator and you are left with:

A2 / A1 = x^2

x is the common ratio of the corresponding parts.

x^2 is the square of the ratio of the coresponding sides.

RELATED QUESTIONS
Prove that the ratio of the areas of 2 similar triangles is equal to the square of the... (answered by math_helper)

The ratio of the areas of two similar triangles is 25:36. What is the ratio of the... (answered by rapaljer)

The ratio of the areas of two squares is 3 : 4. What is the ratio of the lengths of... (answered by Fombitz)

The ratio of corresponding sides in two similiar triangles is 5:4. What is the ratio of... (answered by rapaljer)

The ratio of the areas of two squares is 6:1. find the corresponding ratio of the lengths (answered by josmiceli,edjones)

The areas of two similar triangles are 108 cm² and 972 cm². What is the ratio of the... (answered by greenestamps,ikleyn,Theo)

Two rectangles are similar. The ratio of their corresponding sides is 1:4. Find the... (answered by richard1234)

The ratio of the corresponding sides of two similar triangles is 7:5. Find the ratio of... (answered by Alan3354)