Question

J1 L1- Perimeter Word ProblemsCooper Sha'NiyaThe length of a rectangle is 5 more than twice the width. If the perimeter of the rectangle is 34, what is the length

Answer 1

We can pose the question in the following way:

`l=2w+5`

We have that the perimeter in a rectangle is:

`P=2l+2w`

We can substitute the first equation in the second equation:

`P=2\cdot(2w+5)+2w_{}\Rightarrow P=4w+10+2w\Rightarrow P=6w+10`

Then, we have that P = 34. Thus:

`34=6w+10\Rightarrow6w=34-10\Rightarrow6w=24\Rightarrow w=(24)/(4)\Rightarrow w=6`

We can substitute this value of w = 6 in the first equation, then:

`l=2w+5\Rightarrow l=2\cdot(6)+5\Rightarrow l=12+5\Rightarrow l=17_{}`

Then, the length of the rectangle is l = 17 units.