# 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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