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?

grif389 Jan 6, 2019

#1**+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.

MathsGod1 Jan 6, 2019