Question

The area of a rectangle is twice its breadth. When length is reduced by 3 cm and breadth increased by 2 cm, its area becomes 72cm² . Form an equation relating the length, breadth and area of new rectangle

Answer 1

Answer

• Length is 23 cm
• Breadth is 14 cm

Explanation

Correct Question

The length of a rectangle is 5 cm. less than twice its breadth. If the length is decreased by 3cm and breadth is increased by 2 cm, the perimeter of the resulting rectangle is 72cm. Find the dimensions of the rectangle.

Given

• Area of a rectangle is twice its breadth
• Length is reduced by 3 cm and the breadth is increased by 2 cm then the new perimeter will be 72 cm²

To Find

• Area of the new Rectangle

Solution

The length will be,

➝ Length = 2x - 5

So when the new length will be,

➝ New Length = (2x-5-3)

➝ New Length = (2x-8)

Then the new breadth will be,

➝ New Breadth = (x+2)

✭ Using the Perimeter formula

➝ Perimeter = 2(l+b)

➝ 72 = 2(2x-8+x+2)

➝ 72/2 = 3x-6

➝ 36 = 3x-6

➝ 36+6 = 3x

➝ 42 = 3x

➝ 42/3 = x

➝ x = 14

✭ Original Breadth

➝ Original Breadth = x

➝ Original Breadth = 14 cm

✭ Original Length

➝ Original Length = 2x-5

➝ Original Length = 2 × 14 -5

➝ Original Length = 28-5

➝ Original Length =23 cm