Question

A square piece of paper has an area of x2 square units. A

rectangular strip with a width of 2 units and a length of x
units is cut off of the square piece of paper. The remaining
piece of paper has an area of 120 square units.

Answer 1

Length of rectangular strip = 12

area of rectangular strip = 2*12 = 24

Area of square = x^2 = 12^2 = 144

Explanation:

Area of square x^2

area of rectangle is given by length * width

Length of rectangular strip = x

width of rectangular strip = 2

area of rectangular strip = length * width = 2*x = 2x

Area of square piece of paper when rectangular strip is taken away from it

= Area of square - area of rectangular strip

=
`x^2 -2x`

It is given that Area of square piece of paper when rectangular strip is taken away from it is 120 square units.

Thus,

`x^2 -2x = 120\\=> x^2 -2x -120 = 0\\=> x^2 -12x +10x-120\\=> x(x-12) +10(x-12)\\=> (x+10)(x-12) = 0\\\\`

Thus,

either x+10 = 0 or x -12= 0

x = -10 or x = 12

but length cannot be negative hence neglecting x = -10

hence value of x is 12.

Hence,

Length of rectangular strip = 12

area of rectangular strip = 2*12 = 24

Area of square = x^2 = 12^2 = 144