Question

Length of the floor of a room is one and half times more than the breadth and if the area of the floor is 96 square feet ,what is its length and breadth

Answer 1

Given :

• Length of the floor (l) = 1/2× breadth(b) +b
• Area of the floor = 96 square feet

To Find :

• Length of the floor
• Breadth of the floor

Formula used :

• Area of rectangle = l × b

Solution :

According to the question,

Length (l) = b/2+ (b)

Length (l) = 3b/2

Now,

$Area \: of \: floor = l \times b \\ \\ = > 96 = \frac{3b}{2} \times b \\ \\ = > 96 \times 2 = 3 {b}^{2} \\ \\ = > \frac{96 \times 2}{3} = {b}^{2} \\ \\ = > 64 = {b}^{2} \\ \\ = > \sqrt{64} = b \\ \\ = > 8 = b$

$So,\: breadth (b) = 8 ft$

And,

$Length (l) = \frac{3b}{2} = \frac{3 \times 8}{2} = 12 \: ft$

Therefore, the length of floor is 12 feet and the breadth of the floor is 8 feet.

Answer 2

Given :

• Length of the floor of a room is one and half times more than the breadth.

• The Area of the floor is 96 square feet.

To find :

• Length and Breadth of the floor =?

Step-by-step explanation :

Let, the breadth of the floor be x.

Then, the length of the floor be, x + x/2 = 3x/2.

We know that,

Area of Rectangle = Area of floor = length x breadth

Substituting the values in the above formula, we get,

➮ 96 = 3x/2 × x

➮ 96 = 3x² / 2

➮ 3x² = 96 × 2

➮ x² = 96 × 2/3

➮ x² = 32 × 2

➮ x² = 64

➮ x = √64

ㅤㅤㅤ ____

➮ x = √8 × 8

➮ x = 8

Therefore, We get the value of x = 8.

Hence,

Breadth of the floor = 8 Feet.

Length of the floor, 3x/2 = 3 × 8 / 2

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ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ = 12 Feet.