Question

The area of a room is 168 square feet. If the length is 2 feet
more than the breath find the length and breadth of the
room.​

Answer 1

let breadth = x feet

length = (x+2) feet

A/q ,

area of room = x(x+2) = 168

x²+2x-168 = 0

x²+14x-12x-168 = 0

x(x+14)-12(x+14) = 0

(x+14)(x-12) = 0

x= 12 feet = breadth

length = 14 feet

Answer 2

✬ Length = 14 feet ✬

✬ Breadth = 12 feet ✬

Step-by-step explanation:

Given:

• Area of room is 168 sq feet.
• Length of room is 2 feet more than breadth.

To Find:

• What is the length and breadth of room ?

Solution: Let the breadth of room me x feet. Then

➮ Length of room = 2 feet more than breadth

➮ Length = (x + 2) feet

As we know that room is in the Rectangle shape.

★ Area of Rectangle = ( Length $\times$ Breadth ) ★

A/q

• Area = 168 sq feet

$\implies{\rm }$ 168 = (x + 2) (x)

$\implies{\rm }$ 168 = x² + 2x

$\implies{\rm }$ 0 = x² + 2x – 168

Now, By middle term splitting method-

➫ x² + 2x – 168

➫ x² + 14x – 12x – 168

➫ x (x + 14) – 12 (x + 14)

➫ (x – 12) (x +14)

➫ (x – 12) = 0 & (x + 14) = 0

➫ x = 12 & x = – 14

Since, x is feet and it cannot be negative so take x = 12 feet

Hence,

➳ Breadth of room = x = 12 feet.

➳ Length of room = (x + 2) = 12+2 = 14 feet.