Question

If diagonal of a rectangle is √153 cm and it is given that length of rectangle is four times its breadth,then find area of the rectangle
pls give the answer in step by step explanation​

Answer 1

Answer:

Given :-

• The diagonal of a rectangle is √153 cm

• The length of the rectangle is 4 times its breadth .

To find :-

• The area of the rectangle.

Solution :-

Let the breadth of the rectangle be X cm

Length of the rectangle

= 4 times its breadth

= 4X cm

We know that

The diagonal of a rectangle is

d = √(l²+b²) units

Given that

The diagonal of the rectangle = √153 cm

Therefore, √(l²+b²) = √153

=> √[(4X)²+(X)²] = √153

On squaring both sides then

=> [√{(4X)²+(X)²}]² = (√153)²

=> (4X)²+X² = 153

=> 16X²+X² = 153

=> 17X² = 153

=> X² = 153/17

=> X² = 9

=> X = ±√9

=> X = ±3

Since, X can't be negative.

Therefore, X = 3 cm

Breadth of the rectangle = 3 cm

If X = 3 cm then Length = 4X

= 4(3)

= 12 cm

We know that

Area of a rectangle = length×breadth sq.units

Area of the given rectangle

= 12×3

= 36 cm²

Answer :-

Area of the given rectangle is 36 cm²

Check :-

We have,

Length = 12 cm

Breadth = 3 cm

Length = 4×3 = 4 times the breadth

Diagonal = √(l²+b²) units

=> d = √(12²+3²) cm

=> d = √(144+9) cm

=> d = √153 cm

Verified the given relations in the given problem.

Used formulae:-

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

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

Step-by-step explanation: