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In the staircase-shaped region below, all angles that look like right angles are right angles, and each of the eight congruent sides marked with a tick mark have length 1 foot. If the region has area 53 square feet, what is the number of feet in the perimeter of the region?

MIRB14  Dec 5, 2017

Best Answer 

 #1
avatar+7155 
+1

Let's call the second longest side  x  .

 

 

Now we can see that the figure is a rectangle with  10  square feet removed from it. So...

 

area  =  (9 ft)(x ft)  -  10 ft2

 

area  =  9x ft2  -  10 ft2

 

53 ft2  =  9x ft2  -  10 ft2

 

53  =  9x - 10

 

63  =  9x

 

x  =  7

 

And the perimeter, in feet  =  9 + 7 + 9 + 7  =  32

hectictar  Dec 5, 2017
 #1
avatar+7155 
+1
Best Answer

Let's call the second longest side  x  .

 

 

Now we can see that the figure is a rectangle with  10  square feet removed from it. So...

 

area  =  (9 ft)(x ft)  -  10 ft2

 

area  =  9x ft2  -  10 ft2

 

53 ft2  =  9x ft2  -  10 ft2

 

53  =  9x - 10

 

63  =  9x

 

x  =  7

 

And the perimeter, in feet  =  9 + 7 + 9 + 7  =  32

hectictar  Dec 5, 2017

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