Question

3. The area of a rectangular site is 96 m². If its length is greater than its breadth by 4 metres. The
length and breadth of the said site are-
a) 10 metres, 6 metres b) 12 m and 8 m c) 8 m and 12 m d) 4 m and 8 m



pllzzz help me ​

Answer 1

Let the breadth of the rectangle be x.

Then atq, length will be x+4

We know that,

Area of Rectangle = Length × Breadth.

Therefore,

→ 96 = (x+4) × x

→ 96 = x(x+4)

→ 96 = x² + 4x

Or

x² + 4x - 96 = 0

Now we will solve this quadratic equation.

We need two numbers , such that their product should be -96 and their sum should be 4.

Numbers are 12 and -8

→ x² + 12x - 8x - 96 = 0

→ x(x+12) - 8(x + 12) = 0

→ (x - 8)(x + 12) = 0

If

x - 8 = 0

Then,

x = 8

Or if

x + 12 = 0

→ x = -12

But since breadth of the rectangle can't be negative, therefore x = 8 is the right answer.

Hence, breadth of the rectangle is x = 8m

And length of the rectangle is → x + 4m → 8m + 4m = 12m

Hence, option b is correct (i.e., 12m and 8m).