In a ∆PQR, PQ = PR and PT is perpendicular to QR. If PQ = 17 cm, PT = 15 cm, then what is the measure (in cm) of QR?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 16.
We have an isosceles triangle PQR (PQ = PR).
PT is the altitude from P to QR, dividing QR into two equal segments.
We know PQ = 17 cm and PT = 15 cm.
We need to find the length of QR.
Since triangle PTQ is a right-angled triangle, we can use the Pythagorean theorem: PT² + TQ² = PQ²
Substitute the given values: 15² + TQ² = 17² 225 + TQ² = 289 TQ² = 64 TQ = 8 cm
Find QR:
Since PT bisects QR, we know that QR = 2 × TQ.
Substitute the value of TQ: QR = 2 × 8 QR = 16 cm
Therefore, the measure of QR is 16 cm.