Given:
[tex]\Delta MNO\cong \Delta PQR[/tex]
To find:
The length of QR.
Solution:
We have,
[tex]\Delta MNO\cong \Delta PQR[/tex]
Then, [tex]MN=PQ[/tex] (CPCTC)
[tex]10=4x-2[/tex]
[tex]10+2=4x[/tex]
[tex]12=4x[/tex]
Divide both sides by 4.
[tex]\dfrac{12}{4}=x[/tex]
[tex]3=x[/tex]
Similarity,
[tex]MO=PR[/tex] (CPCTC)
[tex]2y+3=21[/tex]
[tex]2y=21-3[/tex]
[tex]2y=18[/tex]
Divide both sides by 2.
[tex]y=9[/tex]
Now,
[tex]x+y=3+9[/tex]
[tex]x+y=12[/tex]
Therefore, the correct option is d.
