Let's denote the length of the rectangle as L and the width as W. We are given that the width is 7 centimeters less than the length, so W = L - 7.
We are also given that the area of the rectangle is 330 square centimeters, so we can write the equation for the area:
Area = Length x Width
330 = L x (L - 7)
330 = L^2 - 7L
Now we need to solve this quadratic equation. Let's first put it in standard form:
L^2 - 7L - 330 = 0
Now we factorize this equation:
(L + 15)(L - 22) = 0
This gives us two possible solutions: L = -15 or L = 22. Since the length cannot be negative, we discard the -15 solution. Therefore, the length of the rectangle is 22 cm.
Now we can find the width using the equation W = L - 7:
W = 22 - 7
W = 15
Therefore, the dimensions of the rectangle are:
Length = 22 cm
Width = 15 cm
A rectangle has a width that is 7 centimeters less than its length, and its area is 330 square centimeters. What are the dimensions of the rectangle?
length =
centimeters
width =
centimeters
1 answer
1 answer