Question

In the figure below, AMNO

APQR. Determine the length of QR.
M
2y + 3
4x-2
x+ y
R
21
9
O 14
O3
O 12

Answer 1

Given:

`\Delta MNO\cong \Delta PQR`

To find:

The length of QR.

Solution:

We have,

`\Delta MNO\cong \Delta PQR`

Then,
`MN=PQ` (CPCTC)

`10=4x-2`

`10+2=4x`

`12=4x`

Divide both sides by 4.

`(12)/(4)=x`

`3=x`

Similarity,

`MO=PR` (CPCTC)

`2y+3=21`

`2y=21-3`

`2y=18`

Divide both sides by 2.

`y=9`

Now,

`x+y=3+9`

`x+y=12`

Therefore, the correct option is d.