Question

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1. Find the side of a square room such that if its length and width are increased by 4 feet the area is increased by 120 square feet.
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Answer 1

The side of the square room is 13 feet.

GIVEN

Side is increased be 4 feet. The area is increased by 120 Square feet.

TO FIND

The side of the square.

SOLUTION

We can simply solve the above problem as follows;

Let the original side of the square = x feet

So,

Original area of the square = x² feet

Now,

According to the question;

(x + 4)² = x² + 120

Applying the formula; (a+b)² = a² + b² + 2ab

x² + 16 + 8x = x² + 120

8x = 120-16

8x = 104

x = 13

Hence, The side of the square room is 13 feet.

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Answer 2

The length of the side of the square room is equal to 13 feet.

Given:

When the length and width of a room are increased by 4 feet, the area is increased by 120 square feet.

To Find:

The length of the side of the square room.

Solution:

→ Let the length of the side of the square room be 's'.

→ Let the initial area of the square room be 'A'.

   ∴ The initial area of the square (A) = s² - Eq.(i)

→ When the length and width of a room are increased by 4 feet, the area is increased by 120 square feet:

  ∴ (s + 4)(s + 4) = A + 120

  ∴ s² + 4s + 4s + 16 = A + 120

  ∴ s² + 8s = A + 104

→ Putting the value of 'A' from equation (i):

  ∴ s² + 8s = (s²) + 104

  ∴ 8s = 104

  ∴ s = 13 feet

→ The value of 's' comes out to be equal to 13 feet.

Therefore the length of the side of the square room is equal to 13 feet.

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