Question

The length of a rectangle is 8 cm greater than its width. Find the dimensions of the rectangle if its area is 105 cm.
How do I solve?

Answer 1

Area = Length*Width

Information you are given:
Area = 105cm^2
and
Length = width + 8

therefore:

105 = (width + 8)*width
105 = width^2 + 8*width

105 = w^2 + 8w
rearranging we get a quadratic:

w^2 + 8w - 105 = 0
w^2 - 7w +15w - 105 = 0
w(w - 7) + 15(w - 7) = 0
(w - 7)(w + 15) = 0
The two possible solutions are
width = 7 or width = -15

Well, the width must be a positive measurement so we take the width = 7

So the answer is:
Width = 7
Length = 7 + 8 = 15

Ok,
Hope that helps

Answer 2

The width of a rectangle is 34 units less than its length period if x is the rectangle's length, then it's area is?