## AREA OF RECTANGLE

Area of rectangle :

Here we are going to see how to find the area of any rectangle. Here we give clear explanation about rectangle.

## Definition of rectangle

A plane figure with four straight sides and four right angles.In which the opposite sides are having the same length. Formula:

Area of rectangle  =  L x B

Here "L" represents length of the rectangle and "B" represents the breadth of the rectangle.

Problem 1:

Find the area of the rectangle whose length is 15 cm and breadth is 20 cm.

Solution :

Area of a rectangle  =  L x B

Here length (l) = 15 cm and breadth = 20 cm

=  15 x 20

=  300 cm²

Problem 2 :

Find the area of the rectangle having the diagonal is measuring 13 cm and length measuring 12 cm.

Solution :

The diagonal divides the rectangle into two right triangle. In the right triangle ABC the right angled at B. The side which is opposite to 90°degree is called hypotenuse side. By using Pythagorean theorem

AC² = AB² + BC²

13² = 12² + BC²

169 = 144 + BC²

169 - 144 = BC²

25 = BC²

BC = √25

BC = √5 x 5

BC = 5

So, breadth of the rectangle = 5 cm

Area of the rectangle = Length x Breadth

= 12 x 5

= 60 cm²

Problem 3 :

The length and breadth of the rectangle are in the ratio 5:2 .If the area of the rectangle is measuring 147 cm². Then find the length and breadth of the rectangle.

Solution :

5x and 2x be the length and breadth of the rectangle respectively.

Area of the rectangle = 147 cm²

Length x breadth  =  147

5x x 2x  =  147

7x²  =  147

x²  =  147/7

x²  =  21

x  =  √21

Length  =  5x  =  5√21 cm

Breadth  =  2x  =  2√21 cm

Problem 4 :

Find the cost of carpeting a room 13 m long and 9 m broad with a carpet 75 cm wide at the rate of \$12.40 per square meter.

Solution :

From the given information we come to know that

Area of carpet  =  Area of room  ---- (1)

area of rectangle  =  length  x breadth

0.75 x breadth of carpet  =  13 x 9

breadth of carpet  =  (13 x 9) /0.75

=  117/0.75

=  156 m

Cost of carpeting = 156 x 12.40 = \$ 1934.40

Problem 5:

If the diagonal of a rectangle is 17 cm long its perimeter is 46 cm, find the area of rectangle.

Solution :

Let "x" and "y" be the length and breadth of the rectangle respectively.

perimeter of rectangle = 46

2 (x + y) = 46

y = 23 - x -----(1) x² + y² = 17²

x² + y² = 289  -----(2)

Substitute (1) in the second equation

x² + (23- x)² = 289

x² + (23)² + x² - 2 (23)(x) = 289

2x² - 46x + 529 - 289 = 0

2x² - 46 x + 240 = 0

divide the whole equation by 2

x² - 23 x + 120 = 0

(x - 15) (x - 8) = 0

x = 15   x = 8

y = 23 - 15           y = 23 - 8

y = 8  y = 15

So, length of rectangle = 15 m and

breadth of rectangle= 8 m

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