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

Answer:

m = 3

Step-by-step 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.

$\dfrac{AB}{DE} = \dfrac{BC}{EF}\\\Rightarrow \dfrac{3}{2m} = \dfrac{4}{m+5}\\\Rightarrow 3 \times (m+5) = 4 \times 2m\\\Rightarrow 3m +15= 8m \\\Rightarrow 5m=15\\\Rightarrow m = 3$

So, value of m = 3.