Question

In the given figure triangle ABC~ triangle DEF. Find the length of the sides of each triangle.
In triangle Abc
AB= x-1
AC=4x
BC=2x+2

In the triangle DEF
DE=8
DF=8x
EF=3x+9

Please make the figure and give the answer.

Answer 1

this may help to you

Answer 2

We need to recall the following conditions for similar triangles.

If two triangles are similar, then

• The corresponding sides are proportional.
• The corresponding angles are equal.

This problem is about similar triangles.

Given:

Δ ABC ~ Δ DEF

$AB=x-1, AC=4x, BC=2x+2$

$DE=8,DF=8x,EF=3x+9$

Since ΔABC ~ Δ DEF.

The corresponding sides are proportional.

$\frac{AB}{DE}=\frac{AC}{DF}=\frac{BC}{EF}$

$\frac{x-1}{8}=\frac{4x}{8x}=\frac{2x+2}{3x+9}$               ........$(1)$

From equation $(1)$ , we get

$\frac{x-1}{8}=\frac{4x}{8x}$

$\frac{x-1}{8}=\frac{1}{2}$

$x-1=\frac{8}{2}$

$x-1=4$

$x=4-1$

$x=3$

Hence, the dimensions of the triangles are as follows.

For Δ ABC:

$AB=x-1=3-1=2$

$AC=4x=4(3)=12$

$BC=2x=2(3)=6$

For Δ DEF:

$DE=8$

$DF=8x=8(3)=24$

$EF=3x+9=3(3)+9=18$