Question

The triangles are similar. If DE=32, EF=24,and BC=6, find AB

Answer 1

ABC = DEF
AB = DE , AC = DF & BC = EF ( means similar )
EF = 4times BC
So, the triangle DEF is 4times the triangle ABC
EF = 24 and BC = 6
So, AB = DE/4 = 32/4 = 8

Answer 2

The length of AB is 8

Explanation:

The triangle ΔABC and ΔDEF are given as in figure-1

We can observe from given data that,

The length of sides of triangle ΔDEF is 4 times the sides of triangle ΔABC.

ΔABC ≅ ΔDEF

EF=4×BC

⇒ EF=4×(6)=24

DE=4×AB

Divide both sides by '4'

⇒
`(DE)/(4)`=AB

⇒
`(32)/(4)=AB`

⇒ 8=AB

Hence the length of AB is 8