Question

Find the value of m that makes ABC~DEF when AB= 3, BC= 4, DE= 2m, EF= m+5, and ∠B≅∠E.

Answer 1

m = 3

Explanation:

It is given that there are two triangles
`\triangle`ABC and

`\triangle`ABC ~

Also, the sides are:

AB= 3

BC= 4

DE= 2m

EF= m+5 and

∠B≅∠E

Please have a look at the attached figure for
`\triangle`ABC and

The triangles are similar so as per the property of similar triangles, the ratio of corresponding sides will be same.

i.e.

`(AB)/(DE) = (BC)/(EF)\\\Rightarrow (3)/(2m) = (4)/(m+5)\\\Rightarrow 3 * (m+5) = 4 * 2m\\\Rightarrow 3m +15= 8m \\\Rightarrow 5m=15\\\Rightarrow m = 3`

So, value of m = 3.