( 'x' is not 144 .)
The supplement of an angle is (180 - x) .
The problem says that (2/3) of 'x' is equal to (180 - x) .
180 - x = 2/3 x
Multiply each side by 3 :
( Note: 3 x 180 = 540 .)
540 - 3x = 2x
Add 3x to each side:
540 = 5x
Divide each side by 5 :
<u>x = 108°</u> .
1. Let's call:
x: the width of the walkway.
b: 2x+16 (there is a widht "x" of the walkway on each side).
h: 2x+32 (there is a widht "x" of the walkway on each side).
A: 924 ft^2 ( the area of the pool of including the walkway).
2. The area of a rectangle is:
A=(b)(h)
b: the base of the rectangle (2x+16)
a: the height of the rectangle (2x+32)
3. Then, we have a quadratic equation:
924=(2x+16)(2x+32)
4x^2+64x+32x+512-924=0
4x^2+96x-412=0
4. We apply the quadratic formula to find the value of "x":
x=(-b±√(b^2-4ac))/2a
x=3.71
The answer is: The width of the walkway is 3.71 ft
Angle P is an Acute Angle
<em>A</em><em>+</em><em>2</em><em>2</em><em>°</em><em>=</em><em>9</em><em>0</em><em>°</em><em> </em><em>(</em><em>SUM</em><em> </em><em>OF</em><em> </em><em>COMPLEMENTRY</em><em> </em><em>ANGLES</em><em> </em><em>)</em>
<em>A</em><em>=</em><em>9</em><em>0</em><em>°</em><em>-</em><em>2</em><em>2</em><em>°</em>
<em>A</em><em>=</em><em>6</em><em>8</em><em>°</em><em> </em><em>ANSWER</em><em>.</em>
