Question

The ratio of the length and breadth of the rectangle is 5:3 and its perimeter is 144 m . Find the length and breadth of rectangle.

Answer 1

Answer:

• The length and breadth of the rectangle is 45 m and 27 m.

Step-by-step explanation:

Given :-

• The ratio of the length and breadth of the rectangle is 5 : 3 and its perimeter is 144 m .

To Find :-

• Length and breadth of the rectangle.

Basic Terms :-

• Length : Length is a measure of how long an object is or the distance between two points.
• Breadth : Breadth is used to describe the distance from the right side to the left side of a shape.

Formula Used :-

⦾ To find the dimensions we know that,

✦ Perimeter of rectangle = 2(l + b) ✦

where,

• Perimeter of rectangle = 144 m.
• l = length.
• b = breadth.

Solution :-

➊ As we see, that we are given the ratio of length and breadth and the perimeter of the rectangle. So, let us consider the length and breadth of the rectangle be 5x and 3x.

Given :

• Perimeter of the rectangle = 144 m.
• Length = 5x.
• Breadth = 3x.

According to the question by using the formula we get,

↦ Perimeter of rectangle = 2(l + b)

↦ 144 = 2(5x + 3x)

↦ 144 = 10x + 6x

↦ 144 = 16x

↦ x = 144/16

➦ x = 9 m

➋ Now we have the value of x. So, by putting the value of x in the assumed dimensions we will find out length and breadth of the rectangle.

➲ Length = 5x = 5(9) = 5 × 9 = 45 m.

➲ Breadth = 3x = 3(9) = 3 × 9 = 27 m.

∴ Hence, the length and breadth of the rectangle is 45 m and 27 m.

❖ Verification ❖

↦ 144 = 2(5x + 3x)

↦ 144 = 10x + 6x

Putting x = 9 we get,

↦ 144 = 10(9) + 6(9)

↦ 144 = 10 × 9 + 6 × 9

↦ 144 = 90 + 54

↦ 144 = 144

➦ LHS = RHS

∴ Hence, Verified ✔