In Fig. 9.41, the area of ∆PQR is 20 cm² and area of ∆PQS is 44 cm². Find the length RS, if PQ is perpendicular to QS and QR is 5cm.
Solution:
Given, the area of ∆PQR is 20 cm²
The area of ∆PQS is 44 cm²
QR = 5 cm
We have to find the length RS, if PQ is perpendicular to QS.
Area of triangle = 1/2 × base × height
Area of ∆PQR = 1/2 × QR × PQ
20 = 1/2 × 5 × PQ
PQ = 20(2)/5
= 4(2)
PQ = 8 cm
Area of ∆PQS = 1/2 × QS × PQ
44 = 1/2 × QS × 8
QS = 44(2)/8
= 44/4
QS = 11 cm
PQ is perpendicular to QS.
So, QS = QR + RS
11 = 5 + RS
RS = 11 - 5
RS = 6 cm
Therefore, RS = 6 cm
✦ Try This: The perimeter of a rhombus is 40 cm. If one diagonal is 16 cm, find its area in cm².
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11
NCERT Exemplar Class 7 Maths Chapter 9 Problem 87
In Fig. 9.41, the area of ∆PQR is 20 cm² and area of ∆PQS is 44 cm². Find the length RS, if PQ is perpendicular to QS and QR is 5cm.
Summary:
In Fig. 9.41, the area of ∆PQR is 20 cm² and area of ∆PQS is 44 cm². The length RS is 6 cm, if PQ is perpendicular to QS and QR is 5 cm.
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