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△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 ? Enter your answer, in simplest form, in the boxes. :

Answer :

calculista
Let
h1---------------> height of △ABC 
b1---------------> base  of △ABC
h2--------------->height of △DEF
b2---------------> base of △DEF

we know that
h1=20 in
h2=24 in

Since they are similar, their bases must be in the same proportion:
h1/b1=h2/b2------> 20/b1=24/b2-----------> 24b1=20b2
b1=20b2/24-------------> equation 1

Area of △ABC=b1*h1/2
Area of △DEF=b2*h2/2

Let
r------>[the ratio of the area of △ABC to the area of △DEF]
r=[b1*h1/2]/[b2*h2/2]------> [b1*h1]/[b2*h2]
r=[20b1]/[24b2]---------------> equation 2

I substitute 1 in 2
r=[20(20b2/24)]/[24b2]--------> r=20²/24²-------> r=0.6944

the answer is 
the ratio of the area of △ABC to the area of △DEF is 0.69

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