Question

A rectangular frame has length (x+2) units and width (x-2) units. If the area is 96 square units, what is the value of x?

Answer 1

x=10

Explanation:

according to the question

(x+2)(x-2)=96

=>x^2-4=96

=>x^2=96+4

=>x^2=100

=>x=√100

Therefore

x=10

x=-10

As width and length can't be negative

So x=10

Width=10-2=8

Length=10+2=12

12×8=96 (proven)

Answer 2

Please check the explanation.

Explanation:

As we know that the area of a rectangle is defined by multiplying the length by the width.

• 
  `A=l* w`

Given

• rectangular frame length = l = (x+2) units

• rectangular frame width = w = (x-2) units

• Area = 96 square units

substituting all the given values in the formula to find the value of x.

`A=l* w`

`96=\left(x+2\right)* \left(x-2\right)`

`96=x^2-4`

`x^2-4=96`

subtract 96 from both sides

`x^2-4-96=96-96`

`x^2-100=0`

`x^2=100`

`\mathrm{For\:}x^2=f\left(a\right)\mathrm{\:the\:solutions\:are\:}x=√(f\left(a\right)),\:\:-√(f\left(a\right))`

`x=√(100),\:x=-√(100)`

`x=10,\:x=-10`

Putting x = -10 in the length and width will make the length and width negative, which can not be possible.

i.e.

length = l = x+2 = -10+2 = -8 units

width = w = x-2 = -10-2 = -12 units

Therefore, x=-10 must be excluded.

Now, putting the length of x = 10.

i.e.

length = l = 10+2 = 10+2 = 12 units

width = w = x-2 = 10-2 = 8

`A=l* w`

96 = 12 × 8

96 = 96

Therefore, the correct value of x = 10