Question

Urgently need this my kid is confused and so am I.

The length, x, of a rectangle is five more than the width, y, and the perimeter of the rectangle is 42 meters. If y = x – 5 is one equation used to solve the system of equations, select the other equation that can be used to solve the for the length and width of the rectangle. What are the values of the length and width?

Answer 1

The other equation is
`x + y = 21`

The length and width are 13 and 8

Explanation:

Given

`Perimeter = 42`

`y = x - 5`

Required

What is the other equation for the length and width?

x and y represents the length and width respectively.

The perimeter of a rectangle is calculated using:

`Perimeter = 2 * (length + width)`

In this case, it is:

`Perimeter = 2 * (x + y)`

Substitute 42 for perimeter

`42 = 2 * (x + y)`

Divide through by 2

`21 = x + y`

`x + y = 21`

Required: The values of length and width

We have that:

`y = x - 5`

`x + y = 21`

Substitute x - 5 for y in the second equation

`x + x - 5 = 21`

`2x - 5 = 21`

Add 5 to both sides

`2x - 5 + 5 = 21 + 5`

`2x = 26`

Divide through by 2

`x = 13`

Substitute 13 for x in
`y = x - 5`

`y = 13 - 5`

`y = 8`

Hence, the length and width are 13 and 8 respectively