Question

The width of a rectangle is the length minus 2 units. The area of the rectangle is 48 units. What is the width, in units, of the rectangle?

Answer 1

6 units

Explanation:

Remember the formula for the area of a rectangle: A = lw

What we know:

A=48

w = l-2

Substitute A for 48 and w for l-2 into the equation

A = lw

48 = l(l-2) Use the distributive property. Multiply over the brackets.

48 = l² - 2l

Rearrange the equation to standard form (0 = ax² + bx + c) to use quadratic formula.

0 = l² - 2l - 48

a = 1 ; b = -2 ; c = -48 State the variables for the quadratic formula

Substitute a, b and c to find the length:

`l = \frac{-b± \sqrt{b^(2)-4ac} }{2a}`

`l = \frac{-(-2)± \sqrt{(-2)^(2)-4(1)(-48)} }{2(1)}` Simplify

`l = (2± √(4-(-192)) )/(2)`

`l = (2± √(196) )/(2)`

`l = (2± 14 )/(2)`

Split the equation at the ± for adding and subtracting. Then decide which answer is correct, or if both of them are possible answers.

`l = (2- 14 )/(2)`

`l = (-12 )/(2)`

`l = -8` This is "inadmissable", or impossible because the length can't be a negative value.

`l = (2+ 14 )/(2)`

`l = (16 )/(2)`

`l = 8` Length of the rectangle

Use the formula for the area of a rectangle

Substitute the length and area, then isolate "w" for the width

A = lw

48 = (8)w

48/8 = w

w = 6

Therefore the length of the rectangle is 6 units.