Question

Triangle KMN is congruent to triangle PRT. Find the value of x.

Answer 1

We are given that

triangle KMN and triangle PRT are congruent

so, their corresponding sides must be equal

so, we can get

`KM=PR`

`MN=RT`

`NK=TP`

we are given

`KM=15`

`MN=20`

`NK=25`

`RT=3x-1`

now, we can plug this value

`MN=RT=3x-1`

`20=3x-1`

now, we can solve for x

Add 1 on both sides

`20+1=3x-1+1`

`21=3x`

Divide both sides by 3

and we get

`x=7`..............Answer

Answer 2

Congruent triangles have congruent sides and angles. If ΔKMN≅ΔPRT (given) then from the diagram you can conclude that

• KM≅PR;
• MN≅RT;
• KN≅TP.

If MN≅RT, then

3x-1=20,

3x=20+1,

3x=21,

x=21:3,

x=7.

Answer: x=7.