Question

The length of a pen is 5 more than its width.The perimeter is 26 m.Find the length and the width.

Answer 1

P=2l+2w

Since it is given that P=26m, length is 5 more than its width (w+5), we'll work it out in the perimeter formula.

26=2(w+5)+2w
26=2w+10+2w
26=4w+10
4w=26-10
4w=16
w=4

Thus the width is 4m. Let's find the length.

l=w+5
l=4+5
l=9

The length of a pen is 9m.

Answer 2

L = length

W = width

P = perimeter

P = 26m

L = W + 5     [the length is 5 more than the width]

The perimeter is the total of adding all of the side lengths together.

P = L + L + W + W  or  P = 2L + 2W

Because L = W + 5, you can substitute/plug in (W + 5) for "L" in the equation

P = 2L + 2W

P = 2(W + 5) + 2W     Multiply 2 into (W + 5)

P = 2W + 10 + 2W      Combine like terms

P = 4W + 10      

Since you know the perimeter is 26, plug 26 in for "P"

26 = 4W + 10           Subtract 10 on both sides

16 = 4W              Divide 4 on both sides

4 = W

Now that you know the width, you can find the length

L = W + 5

L = 4 + 5

L = 9

The width is 4 m, the length is 9 m.