Question

Given ^MNO = ^PQR,

MN = 6 +2y, MO = 2x + 1,
PO = 3y + 4, and PR = 10 - X.
Find the lengths of PQ and PR.​

Answer 1

Part 1)
`PQ=10\ units`

Part 2)
`PR=7\ units`

Explanation:

The correct question is

The triangles MNO and PQR are congruent. (MNO≅PQR)

Find the lengths of PQ and PR.

we know that

If two figures are congruent, then its corresponding sides are congruent

In this problem

MN and PQ are corresponding sides

MO and PR are corresponding sides

NO and QR are corresponding sides

therefore

MN≅PQ

MO≅PR

NO≅QR

step 1

Find the value of y

we have

`MN = 6 +2y\\ PQ = 3y + 4`

equate the equations

`3y + 4=6 +2y`

solve for y

`3y-2y=6-4`

`y=2`

step 2

Find the length of PQ

`PQ = 3y + 4`

substitute the value of y

`PQ = 3(2) + 4=10\ units`

step 3

Find the value of x

we have

`MO = 2x + 1\\PR = 10 - x`

equate the equations

`2x+1=10-x`

solve for x

`2x+x=10-1`

`3x=9`

`x=3`

step 4

Find the length of PR

`PR = 10 - x`

substitute the value of x

`PR = 10-3=7\ units`