Ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4 (Fig. 9.33). If the area of ∆ WXZ is 56 cm² and WY = 8 cm, find the lengths of XY and YZ.

Solution:

Given, the ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4

The area of ∆ WXZ is 56 cm² and WY = 8 cm.

We have to find the lengths of XY and YZ.

Area of triangle = 1/2 × base × height

Area of ∆ WXY : area of ∆ WZY = 3 : 4

1/2 × XY × WY : 1/2 × YZ × WY = 3 : 4

XY : YZ = 3 : 4

Area of ∆ WXZ = 1/2 × XZ × WY

56 = 1/2 × XZ × 8

56 = 4 × XZ

XZ = 56/4

XZ = 14 cm

From the figure,

XZ = XY + YZ

YZ = XZ - XY

YZ = 14 - XY

Now, XY/YZ = 3/4

XY / (14 - XY) = 3/4

XY(4) = 3(14 - XY)

4XY = 3(14) - 3XY

4XY + 3 XY = 3(14)

7XY = 3(14)

XY = 3(14)/7

XY = 3(2) = 6 cm

YZ = 14 - 6 = 8 cm

Therefore, the lengths of XY and YZ are 6 cm and 8 cm.

✦ Try This: The adjoining figure represents a rectangular lawn with a circular flower bed in the middle. Find the area of the flower bed.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 11

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NCERT Exemplar Class 7 Maths Chapter 9 Problem 79

Ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4 (Fig. 9.33). If the area of ∆ WXZ is 56 cm² and WY = 8 cm, find the lengths of XY and YZ.

Summary:

Ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4 (Fig. 9.33). If the area of ∆ WXZ is 56 cm² and WY = 8 cm, the lengths of XY and YZ are 6 cm and 8 cm.

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