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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
avatar+4682 
+3

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
avatar+94209 
+2

Excellent, MG  !!!

 

 

cool cool cool

 
CPhill  Jan 6, 2019

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