Question

The measures of two adjacent sides of a rectangle are in the ratio 5: 3. If the perimeter of the rectangn
is 80 m, find its length and breadth

Answer 1

Answer:

Given :-

• The measures to two adjacent sides of a rectangle are in the ratio of 5 : 3 and its perimeter is 80 m.

To Find :-

• What is the length and breadth of a rectangle.

Formula Used :-

✪ Perimeter of a rectangle = 2(L + B) ✪

where,

• L = Length
• B = Breadth

Solution :-

Let, the length be 5x

And, the breadth will be 3x

According to the question by using the formula we get,

⇒ $\sf 2(5x + 3x) =\: 80$

⇒ $\sf 2(8x) =\: 80$

⇒ $\sf 16x =\: 80$

⇒ $\sf x =\: \dfrac{\cancel{80}}{\cancel{16}}$

➠ $\sf\bold{\red{x =\: 5\: m}}$

Hence, the required length and breadth are,

✧ Length = 5x = 5(5) = 25 m

✧ Breadth = 3x = 3(5) = 15 m

∴ The length and breadth of a rectangle is 25 m and 15 m respectively.

Let's Verify :-

↦ 2(5x + 3x) = 80

↦ 2(8x) = 80

↦ 16x = 80

Put x = 5 we get,

↦ 16(5) = 80

↦ 80 = 80

➦ LHS = RHS

Hence, Verified ✔

Answer 2

Given

• Measures of two adjacent sides of a rectangle are in the ratio of 5:3
• Perimeter of the Rectangle is 80 m

_____________________________

To Find

• The Length
• The Breadth

_____________________________

Solution

Let the length be 5x and breadth be 3x (Here we have taken 5x and 3x since the length and breadth are in the ratio of 5:3)

Perimeter of rectangle ⇒ 80 m

Formula to find the perimeter of rectangle ⇒ 2 (Length + Breadth)

We'll solve this equation to find the length and breadth → 2 (5x + 3x) = 80

Let's solve your equation step-by-step.

2 (5x + 3x) = 80

Step 1: Simplify the equation.

⇒ 2 (5x + 3x) = 80

⇒ 10x + 6x = 80

⇒ 16x = 80

Step 2: Divide 16 from both sides of the equation.

⇒ 16x ÷ 16 = 80 ÷ 16

⇒ x = 5

∴ The value of 'x' is 5

∴ Length ⇒ 5x ⇒ 5(5) ⇒ 25 m

∴ Breadth ⇒ 3x ⇒ 3(5) ⇒ 15 m

_____________________________