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Attempt following question by selecting a choice to answer. f ΔPQR is congruent to

ΔRST. PR is the longest side of

ΔPQR, PQ = 9 in. and PR = 15 in.. What is the measure of

QS? fff fff A.

f 26 in.

B.

f 24 in.

C.

f 12 in.

D.

f 24 in.

ff
D

Step 1: In the figure, PQR is a right triangle. Step 2: PR is the longest side of PQR Step 3: According to Pythagorean theorem, in a right triangle, hypotenuse^{2} = sum of the squares of other two sides.
Step 4: [Since, PQR is a right triangle]PR^{2} = PQ^{2} + QR^{2} Step 5: [Subtract PQ^{2} from both sides.]QR^{2} = PR^{2} - PQ^{2} Step 6: QR^{2} = 15^{2} - 9^{2} = 225 - 81 = 144 Step 7: QR = √144= 12 in. Step 8: [Since, ΔPQR ≅ ΔRST]QR ≅ RS Step 9: QR = RS = 12 in. Step 10: From the figure, QS = QR + RS Step 11: QS = 12 + 12 = 24[Substitute QR = 12 and RS = 12] Step 12: So, QS = 24 in.