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Answer 1 · 2017-10-17T01:35:21

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

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.