The areas of two similar triangles are 75m2 and 300m2. The length of one of the sides of the second triangles is 9m. What is the length of the corresponding side in the first triangle?

4.5 m

Step-by-step explanation:

The formula for area of a triangle is A = (1/2) bh. If we scale the base and height by a factor of 2, we get ...

A = (1/2) (2b) (2h)

A = 2bh

so 2bh is the new area, comparing it to (1/2) bh of the original triangle gives us

2bh = (1/2) bh (x) (here x is the value we need to multiply (1/2) by by

to get 2bh)

Solve for x

4bh = bhx (multiply both sides by 2 to get rid of the fraction)

4 = x (divide both sides by bh)

The new area is 4 times the area of the original triangle.

Since 300 is four times larger than 75, the side lengths of the original triangle are doubled, so the side of the first triangle is 4.5