Question

The diagonal of a rectangle is 2under root 13cm.If its length and breadth are in the ratio 3:2, then find its area.​

Answer 1

Given :-

The diagonal of a rectangle is 2 √13 cm .

The length and breadth are in the ratio 3:2 .

To find :-

The Area of the rectangle.

Solution :-

Given that

The ratio of the length and breadth of a rectangle = 3:2

Let they be 3X cm and 2X cm

We know that

The diagonal of a rectangle = √(l²+b²) units

The diagonal of the rectangle

= √[(3X)²+(2X)²] cm

= √(9X²+4X²) cm

=> √(13X²) cm

=> √13 X cm

According to the given problem

The diagonal of the rectangle = 2√13 cm

=> √13 X = 2 √13

=> X = 2 √13/√13

=> X = 2 cm

If X = 2 cm then 3X = 3(2) = 6 cm

If X = 2 cm then 2X = 2(2) = 4 cm

Length = 6 cm

Breadth = 4 cm

We know that

Area of a rectangle = length×breadth sq.units

Area of the given rectangle

= 6 cm × 4 cm

= 24 cm²

Answer :-

Area of the rectangle is 24 cm²

Used formulae:-

♦ The diagonal of a rectangle = √(l²+b²) units

♦ Area of a rectangle = length×breadth sq.units

• l = length
• b = breadth

Answer 2

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Given :

The diagonal of a rectangle is 2 ✓13 cm.

The length and breadth are in the ratio

3:2.

To find :

The Area of the rectangle.

Solution :

Given that

The ratio of the length and breadth of a rectangle = 3:2

Let they be 3X cm and 2X cm

We know that

The diagonal of a rectangle = √(1²+b³)

units

The diagonal of the rectangle

= √[(3X)³+(2X)³] cm

= √(9x³+4x²) cm

=> √(13X²) cm

=> √13 X cm

According to the given problem

The diagonal of the rectangle = 2√13 cm

=> ✓13 X = 2 √13

=> X = 2√13/√13

=> X = 2 cm

If X = 2 cm then 3X=3(2) = 6 cm

If X = 2 cm then 2X = 2(2)=4 cm

Length = 6 cm

Breadth = 4 cm

We know that

Area of a rectangle = length breadth sq.units

Area of the given rectangle = 6 cm x 4 cm

= 24 cm²

Answer :

Area of the rectangle is 24 cm²

Used formulae: *The diagonal of a rectangle = √(1²+b³)

units

+ Area of a rectangle = length breadth sq.units

• 1 = length

. b = breadth