Question

In triangles △ABC and △DEF,

m∠A=m∠E, m∠C=m∠F,

AC=6, EF=2, and AB=3.3,

side DF is shorter than side BC by 3.2.

Find the unknown sides of these triangles.

Answer 1

• BC = 4.8
• ED = 1.1
• DF = 1.6

Explanation:

Since angles A and E correspond, as well as angles C and F, we can say ...

ΔABC ~ ΔEDF

Then the ratio of side lengths of ΔABC to those of ΔEDF is ...

AC/EF = 6/2 = 3

That means ...

ED/AB = 1/3

ED = AB·(1/3) = 3.3·(1/3) = 1.1

For the remaining sides, we have the relation

3·DF = BC

3·(BC -3.2) = BC

2BC - 9.6 = 0 . . . eliminate parentheses, subtract length BC

BC -4.8 = 0 . . . . . divide by 2

BC = 4.8 . . . . . . . . add 4.8

DF = BC·(1/3) = 1.6

The unknown side lengths are BC = 4.8, DE = 1.1, DF = 1.6.