Answer:
2ft wide
Step-by-step explanation:
Total Area = Area of the summing pool + total Area of the walkway.
Area of the summing pool = 15 × 15 = 225ft²
And total area of walkway = 136ft²
∴ total area = 225 + 136 = 361 ft².
Let w = The width of the walkway.
Since the walkway has a uniform width
∴ Total Area of pool and walkway = (15+2w)(15+2w)
⇒ (15+2w)(15+2w) = 361........................(1)
Expanding Equation(1)
15×15 + 15×2w + 2w×15 + 2w×2w = 361
⇒ 225 + 30w + 30w + 4w² = 361................(2)
Rearranging equation(2) above and collecting like terms
4w²+60w = 361-225
4w² + 60w = 136..............................(3)
Dividing all through equation(3) by 4
4w²/4 + 60w/4 = 136/4
w² + 15w = 34..............(4)
rearranging equation(4)
w²+15w -34 = 0
Using factorization method to solve the quadratic equation,
w² + 15w - 34 = 0
Two numbers whose sum give +15 and whose product gives -34
are +17 and -2.
∴ w² -2w +17w -34 =0
grouping the equation,
(w²-2w) + (17w-34) =0
Bringing out the common terms in both bracket.
w(w-2) +17(w-2) =0
since both term in the bracket are the same, take one of the term in the bracket and form a bracket for the outer term i.e
(w-2)(w+17)=0.
Either w-2 =0
w=+2
OR w+17 =0
w=-17.
The right answer is w=+2 as wide can not be negative.
∴ The walkway is 2ft wide.
