Question

The length of a rectangle is thrice its breadth and its perimeter is 144 meters. What is its area

Answer 1

Given :-

Length of the rectangle is thrice the breadth

Perimeter of the rectangle = 144 meters

Required to find :-

• Area of the rectangle ?

Formula used :-

${\text{\red{Area \ of \ the \ rectangle }{\blue{= Length \times Breadth }}}}$

${\text{\red{Perimeter \ of \ the \ rectangle = }{\blue{2 ( Length + Breadth }}}}$

Solution :-

Given information :-

Length of the rectangle is thrice the breadth

Perimeter of the rectangle = 144 meters

We need to find the area of the rectangle

So,

Let the breadth of the rectangle be " x " meters

Length is twice the breadth

So,

Length of the rectangle be " 3x " meters

Using the formula ;

${\text{\red{Perimeter \ of \ the \ rectangle = }{\blue{2 ( Length + Breadth }}}}$

But,

It is given that ; perimeter of the rectangle = 144 meters

So,

144 = 2 ( 3x + x )

144/2 = ( 3x + x )

72 = 4x

This implies ,

=> 4x = 72

=> x = 72/4

=> 18

Hence,

• Breadth of the rectangle = x = 18 meters

• Length of the rectangle = 3x = 3 ( 18 ) = 54 meters

Using these values we can find the area of the rectangle

So,

The formula is ;

${\text{\red{Area \ of \ the \ rectangle }{\blue{= Length \times Breadth }}}}$

Substitute the required values ;

☞ Area of the rectangle = 54 meters x 18 meters

☞ Area of the rectangle = 972 m²

Therefore,

☞ Area of the rectangle = 972 m²

Diagram :-

$\setlength{\unitlength}{6mm} \begin{picture}(0,0) \put(1,1){\line(0,1){5}}\put(1,1){\line(1,0){7}} \put(8,1){\line(0,1){5}} \put(1,6){\line(1,0){7}}\put(2.5,0){ \tt Length = 54 m } \put(8.3,3){ \tt Breadth = 18 m }\end{picture}}$

Answer 2

Answer:

The area of rectangle is 972 m²

Step-by-step explanation:

Let,

The breadth of rectangle = x

The length of rectangle = 3x

So,

The perimeter of rectangle = 2(length + breadth)

⇒ 2(3x + x) = 144

⇒ 6x + 2x = 144

⇒ 8x = 144

⇒ x = 144 / 8

⇒ x = 18

.°. The breadth of rectangle = 18

The length of rectangle = 3x

⇒ 3 (18) = 3 × 18 = 54

Now, find it's area

★ Area of rectangle = length × breadth

⇒ 54 × 18

⇒ 972m²

Therefore,

The area of rectangle is 972 m²