Question

Question #e4fda

Answer 1

The width is `"16 cm"` and the length is `"23 cm"`.

Explanation:

1) Choose a variable to represent the length and another for the width. Here I chose

`x = "length"`

`y = "width"`

2) Write an equation to represent what you know. The length `(x)` is `"7 cm"` more than the width `(y)`, or

`x=y+7`

3) Write an equation for your perimeter. REMEMBER, the perimeter is the total of all four sides, so `2 * "length" * 2 * "width"`. or

`y+y+x+x=78`

which can be written as

`2y+2x="78 cm"`

4) You cannot solve an equation with two unknowns, so replace `x` with `y+7`

5) Now your equation is

`2y+14+2y= "78 cm"`

6) Simply and combine like terms

`4y+14 = "78 cm"`

7) Subtract `14` from both sides to get the variable by itself

`4y = "64 cm"`

8) Divide both sides by `4` to solve to for one `y`

`y = "16 cm"`

9) Now you know the width is `"16 cm"`, `y=16`

10) Plug it back into the equation `x=y+7` to solve for the length

`x=16+7`

`x=23`

The length is `"23 cm"`.

EXTRA: You can plug these variables into the perimeter equation `(2y+2x=78)` to see if it matches to check your answer.