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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

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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?

Dec 5, 2017

#1
+7348
+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

Dec 5, 2017

#1
+7348
+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