Question

The perimeter of a rectangular is 58 cm. The length is 5 more than twice the width.

Set up an expression for the length using w for width.

Set up an equation to find the perimeter.

Solve the equation to find the values of the length and the width (show your work)

Answer 1

a) l = 5 + 2w

b) P = 2(l +w) = 2(5 +2w +w)

c) w = 8 cm, l = 21 cm

Step-by-step explanation:

a) Using w for width, twice the width is 2w, and 5 more than that is 5+2w. This is your expression for l:

... l = 5 + 2w

b) The perimeter is the sum of the lengths of all sides, so is the sum of twice the length and twice the width.

... P = 2(l +w) = 2(5 +2w + w) . . . . substituting for l using the expression of (a)

c) Substituting the given perimeter, we have ...

... 58 = 2(5 +3w) = 10 + 6w . . . . . collect terms, eliminate parentheses

... 48 = 6w . . . . . . . . . . . . . . . . . . subtract 10

... 8 = w . . . . . . . . divide by 6

... l = 5 + 2·8 = 21 . . . . . find length using the formula for it

Dimensions are in centimeters, so we can write the solution as ...

• width = 8 cm
• length = 21 cm