+64 A rectangular swimming pool is bordered by a concrete patio. The width of the patio is the same on every side. The area of the surface of the pool is equal to the area of the patio.
What is the width of the patio?
+129847 The area of the pool = 24 * 16 = 384 sq ft
So the total area = twice this = 768 sq ft
Call the patio width, x
So.....the whole area can be represented by
[24 + 2x] * [ 16 + 2x] = 768 simplify
384 + 80x + 4x^2 = 768 divide through by 4
96 + 20x + x^2 = 192 subtract 192 from both sides and rearrange
x^2 + 20x - 96 = 0 factor
[x + 24] * [ x - 4] = 0 set each factor to 0 ..... and we have that
x = -24 or x = 4 reject the negative answer
So.....the patio width = 4 ft
