△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. :
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
