Question

A square placemat has an area of 169 in.² Sally decides to decorate the placemat by putting fringe around the edges how many inches of fringe will Sally need to buy how many feet is this

Answer 1

4 feet and 4 inches of fringe

Explanation:

The length and width of a square are equal to each other

Let x = length of a side of a square

Area of a square = Length × Width

= (x inches) × (x inches)

=
`x^(2)`
`in^(2)`

The area of the square placemat = 169
`in^(2)`

∴
`x^(2) in^(2)` = 169
`in^(2)`

Taking the square root on both sides of the equation to get rid of the square:

x inches =
`√(169)` inches

x inches =
`√(169)` inches

(
`√(169) =` ± 13. However, the negative value will be rejected since the length of a side CANNOT be negative)

So, x = 13 inches

This means the perimeter of the square = (13 + 13 + 13 + 13) inches

= 52 inches

∴ 52 inches of fringe will be needed by Sally

Unit conversion:

I foot = 12 inches

∴ y feet = 52 inches

Cross-multiplication is applied:

(y feet)(12 inches) = (52 inches)(1 foot)

Isolating y and making it the subject of the formula:

y feet =
`((52 inches)(1 foot))/(12 inches)`

Inches in the numerator and denominator will cancel each other out completely:

y feet =
`(52)/(12)` feet

Applying long division:

The highest quotient to be multiplied by 12 to give a number, which is closest to 52 but still less than 52. 12×4 = 48. Therefore, the quotient is 4 and the remainder is 4.

∴ 52 inches = 4 feet and 4 inches