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is congruent to ΔRST. PR
is the longest side of ΔPQR, PQ = 9 in. and PR = 15 in..
What is the measure of QS?B 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,
hypotenuse2 = sum of the squares of other two sides.
Step 4: [Since, PQR is a right triangle]PR2 = PQ2 + QR2
Step 5: [Subtract PQ2 from both sides.]QR2 = PR2 - PQ2
Step 6: QR2 = 152 - 92= 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.