Question
Download Solution PDFTwo medians QT and RS of the triangle PQR intersect at G at right angles. If QT = 18 cm and RS = 27 cm. then the length of QS is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
The medians QT and RS intersect at right angles.
QT = 18 cm, RS = 27 cm
Concept used:
The centroid is the intersection point of all three medians.
Centroid divides the median in the ratio 2 : 1
Calculation:
The two medians intersect at G. Hence G is the centroid of the triangle and the centroid divides the median in the ratio 2 : 1
∴ QG : GT = 2 : 1 ⇒ QG = 18 × 2/3 = 12 cm
Also, RG : GS = 2 : 1 ⇒ GS = 27 × 1/3 = 9 cm
∴ In ΔGQS, ∠QGS = 90° (∵ medians intersect at 90°)
Using Pythagoras theorem,
QG2 + GS2 = QS2
⇒ 122 + 92 = QS2
⇒ QS2 = 225
⇒ QS = √ 225 = 15 cm.
∴ The length of QS = 15 cm.
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