A certain rectangle has a width that is half the difference of the length and 6 cm If the Perimeter of the rectangle is 87 cm what is the length and width of the rectangle?

Answer 1

Algebra works great here. Let's use three variables: P for perimeter, L for length and W for width. Then we can rewrite the above in terms of math:

W = (1/2)(L - 6) <-- Two parentheses together means multiply

P = 87

But what is the perimeter in terms of the length and width? Two lengths and two widths, or:

P = 2L + 2W

Now let's use substitution. We know what the width is in terms of length, and we know the perimeter. So let's replace the variables P and W:

87 = 2L + 2(1/2)(L - 6)

87 = 2L + L - 6

87 = 3L - 6

93 = 3L

31 = L

Now we know that the length is 31 cm. From here, it isn't hard to figure out the width. We'll use our very first equation, the one regarding width, and substitute for L:

W = (1/2)(L - 6)

W = (1/2)(31 - 6)

W = (1/2)(25)

W = 12.5

Thus,

Length = 31 cm

Width = 12.5 cm