Question

The areas of two similar triangles are 9cm2, and 49cm2. One of the sides of the first triangle is 2cm. What is the length of the corresponding side of the other triangle?

Answer 1

4 2/3 cm

Explanation:

When we have area, it is the related to the scale factor by the scale factor squared

Area large/ area of small = 49/9

Take the square root

sqrt(49/9) = 7/3

The scale factor is 7/3 large to small

The small side is 2 cm

large 7 x cm

-------- = ------ = -----------

small 3 2 cm

Using cross products

7*2 = 3x

Divide by 3

14/3 = 3x/3

14/3 = the large side

4 2/3 cm