Question

Triangles ABC and KMN are similar. Find the lengths of the sides of the triangle KMN, if AB=4 cm, BC=5cm, CA=7 cm and KM/AB =2.1.

Answer 1

`KM=8\,cm\\MN=10\,cm\\KN=14\,cm`

Explanation:

Two figures are said to be similar if their shapes are same but they differ in size .

We know that if two triangles are similar then their sides are proportional and angles are equal .

It's given that triangles ABC and KMN are similar .

In symbolic form ,

`\bigtriangleup ABC\sim \bigtriangleup KMN`

We need to find the lengths of the sides of the triangle .

We have
`(KM)/(AB)=(MN)/(BC)=(KN)/(AC)`

Given :
`(KM)/(AB)=(2)/(1)`

AB=4 cm, BC=5cm, CA=7 cm

Therefore,
`(KM)/(AB)=(MN)/(BC)=(KN)/(AC)=(2)/(1)`

we get ,

`KM=2AB=2(4)=8\,cm\\MN=2BC=2(5)=10\,cm\\KN=2AC=2(7)=14\,cm`

Answer 2

KM=8.4 MN=10.5 KN=14.7

Explanation:

They give us the scale factor of dilation with the 2.1. This means that triangle KMN is 2.1 times bigger than triangle ABC. We will then multiply each side by the scale factor and apply that to the corresponding sides of KMN.

AB=KM AB=4

4 * 2.1 = 8.4 KM=8.4

BC=MN BC=5

5 * 2.1 = 10.5 MN=10.5

AC=KN AC=7

7 * 2.1 = 14.7 KN=14.7