Question

△ABC∼△DEF , △ABC has a height of 20 inches, and △DEF has a height of 24 inches. What is the ratio of the area of △ABC to the area of △DEF ?

Answer 1

Let
b1-------------> base △ABC
b2-------------> base △DEF
A1-----------> area △ABC
A2-----------> area △DEF

we know that
h1=20 in
h2=24 in
A1=b1*20/2-------------> A1=10b1
A2=b2*24/2 ------------> A2=12 b2

if △ABC∼△DEF
then
b1/20=b2/24------------> b1=b2*[20/24]-----> b1=b2*[5/6]

What is the ratio of the area of △ABC to the area of △DEF?
A1=10b1
A2=12b2
A1/A2=(10/12)*(b1/b2)-------> (10/12)*(b2*(5/6)/b2)-----> (10/12)*(5/6)=50/72

A1/A2=50/72--------> 25/36

the answer is (25/36)