Question

A pair of adjacent sides of a rectangle are in the ratio 3:4. If its diagonal is 20 cm.Find
the lengths of the sides and hence ,the perimeter of the rectangle.
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Answer 1

Step-by-step explanation:

Given length:breadth = 4:3

Let length = 4x and breadth = 3x

Diagonal = 25 cm

Since the diagonal and the two adjacent sides of a rectangle form a right angled triangle

By Pythagoras theorem, we have

252 = (4x)2 + (3x)2

625 = 16x2 + 9x2 = 25x2

⇒ x2 = 25

∴ x = 5

Hence length = 4x = 20 m and breadth = 3x = 15 m

Perimeter of rectangle = 2(length + breadth)

= 2(20+15) = 70 m

Answer 2

Answer:

Given length:breadth = 4:3

Let length = 4x and breadth = 3x

Diagonal = 20 cm

Since the diagonal and the two adjacent sides of a rectangle form a right angled triangle

By Pythagoras theorem, we have

20² = (4x)2 + (3x)2

400 = 16x2 + 9x2 = 25x2

⇒ x2 = 16

∴ x = 4

Hence length = 4x = 16 m and breadth = 3x = 12 m

Perimeter of rectangle = 2(length + breadth)

= 2(16+12) = 56 m

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