Question

I have 2 similar right angle triangles, CDE and ADG. The length of CDE's hypotenuse is 1/3 the length of ADG's hypotenuse. The area of CDE is 42. What is the area of ADG?

Answer 1

lengths are in ratio 1:3
areas are in ratioo 1 : 3^2 = 1: 9
area of adg = 9 * 42 = 378

Answer 2

Thank you! Can you explain why the areas are in ratio 1 : 3^2 ?

Answer 3

im afraid i cant explain - ill have to check that out

Answer 4

How did you know to go to that ratio?

Answer 5

www.mathopenref.com/similartrianglesareas.html

- the smaller triangle had hypotenuse of 1/3 of larger
so ratio smaller: bigger was 1:3
the corresponding sides must be used ie in this case the two hypotenuse

Answer 6

The 2 legs of a right triangle are the base and the height of the triangle. Area of triangle is (1/2) base * height.
Since both are 3 times bigger in the larger triangle, you get 3*3=9 times more area.

Answer 7

the ratio of two areas would be calculated same way for any two triangles - not just right angled
in fact its true for any two similar shapes