On this page "area of rectangle", we are going to see how to find the area of any rectangle. Here we give clear explanation about 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:**

Let 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

x + y = 23

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

**Related Topics**

**Perimeter of sector****practice questions with solution****Length of arc****Practice questions on length of arc****Perimeter of square****Perimeter of parallelogram****Perimeter of rectangle****Perimeter of triangle****Area of a circle****Area of Semicircle****Area of Quadrant****Area of sector****Area of triangle****Area of equilateral triangle****Area of scalene triangle****Area of square****Area of parallelogram****Area of rhombus****Area of trapezium****Area of quadrilateral****Area around circle****Area of pathways****Area of combined shapes**

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