+0

# help

0
874
2
+165

A rectangular patio has an area of 180 square feet and a perimeter of 54 feet. What is the length of the diagonal (in feet) squared?

Jan 6, 2019

#1
+4695
+4

So,

Area= 180ft

Perimeter= 54ft

Simply meaning, two numbers that multiply to give 180 and add (x2 due to 4 sides) to give 54.

EG

$$\\X ⋅ Y\\ \\X+X+Y+Y\\$$

Factors of 180:

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,60,90,180

Numbers have to be below 54 itself to add up to it

1,2,3,4,5,6,9,10,12,15,18,20,30,36,45,

Find two factors that multiply to 180 that add to 54 (all 4 sides)

12 and 15

12*15= 180

12+12+15+15=54

Length must be 15ft

By diagonal, I assume you mean a diagonal line intersecting through the rectangle (unless you only mean the length of the patio itself).

$$\\12^2+15^2=369\\ \\\sqrt{369}=19.2ft\\$$

When squared that would be 369ft.

Jan 6, 2019
edited by MathsGod1  Jan 6, 2019
edited by MathsGod1  Jan 6, 2019
edited by MathsGod1  Jan 6, 2019
#2
+111466
+2

Excellent, MG  !!!

CPhill  Jan 6, 2019