+166 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?
+4709 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.
