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

#1**+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 ft^{2}

area = 9x ft^{2} - 10 ft^{2}

53 ft^{2} = 9x ft^{2} - 10 ft^{2}

53 = 9x - 10

63 = 9x

x = 7

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

hectictar
Dec 5, 2017

#1**+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 ft^{2}

area = 9x ft^{2} - 10 ft^{2}

53 ft^{2} = 9x ft^{2} - 10 ft^{2}

53 = 9x - 10

63 = 9x

x = 7

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

hectictar
Dec 5, 2017