Price of carpet:

Price of carpet:

Square=$10 per yd²

Rectangle=$12 yd²

The square:

A1=Area of the square

L1=length of the side of the square

A1=L²

The rectangle:

A2=Area of the rectanble

L=length of the rectangle

W=width of the rectangle

A2=LW

The length was 5/4 the width

or simply:

The Combined Area of the two was 405 ft²

A1+A2=405ft²

L²+LW=405ft²

L²+

=405ft²

=405ft²

Multiply both sides by 5

9L²=2025

Divide both sides by 9

L²=225ft²

Square root both sides

L=15ft

Now find the width of the rectangle:

L=

15ft=

Multiply both sides by 4

60ft=5W

Divide both sides by 5

W=12ft

Now find the area of the rectangle:

A2=LW

A2=15ft(12ft)

A2=180ft²

Substitute to the equation to find the area of the square

A1+A2=405ft²

A1+180ft²=405ft²

Subtract both sides by 180ft²

A1=225ft²

Now substitute the value of A1

L²=225ft²

Square root both sides

L=15ft

I don't think the price is useful for this question. But hope this helps =)