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Question

Rectangle has a 5 units, whats is the value of x and are of rectangle ?

Answer 1

From the figure,

Length of the rectangle l is 3/(x+2)

breadth of the rectangle b is 2/(x-3)

Perimeter of the rectangle is 5 units.

We know that Perimeter of a rectangle is 2(l+b)

2(3/(x+2) + 2/(x-3)) = 5

Multiply each side by (x-3)(x+2)

2(3(x-3)+2(x+2)) = 5(x-3)(x+2)

2(3x-9+2x+4) = 5(x²-3x+2x-6)

2(5x-5) = 5(x²-x-6)

10x-10 = 5x²-5x-30

5x²-5x-30 - (10x-10) = 0

5x²-5x-30 - 10x + 10 = 0

5x²-15x-20 = 0

Take out common factor 5.

5(x²-3x-4) = 0

x²-3x-4 = 0

x²-4x + x -4 = 0

x(x-4)+1(x-4) = 0

(x -4)(x + 1) = 0

x = 4, -1

If x = -1 then Breadth of rectangle is negative.

Therefore the value of x is 4.

Length of the rectangle l is 3/(x+2) ⇒ 3/(4+2) ⇒ 3/6 = 1/2 units

Breadth of the rectangle b is 2/(x-3) ⇒ 2/(4-3) ⇒ 2/1 = 2 units

Area of the rectangle is l*b ⇒ (1/2)*2 ⇒ 1 sq-unit.

Therefore,

The value of x is 4 units.

Length of the Rectangle is 1/2 units.

Breadth of the Rectangle is 2 units.

Area of the rectangle is 1 sq-unit.