5ft retangular swimming pool 900=w(w+60)=???

Question

a 5-foot-wide sidewalk around a rectangular swimming pool has a total area of 900 square feet. Find the dimensions of the swimming pool if the pool is 60 feet longer than it is wide.

Answer 1

Draw a rectangle. Label the long side of the rectangle Y, and the short side X. Add a 5' border all the way around it. Divide the border into sections...each of the four corners of the border will be 5' * 5' square. This will leave four rectangles, two of them Y length * 5', and two of them X length * 5'.

 

The area of the border will be the equation 2(5Y) + 2(5X) +100 = 900  

 

NOTE: The 100 comes from the four corners measuring 5' * 5'  --> 4*25 = 100 

 

Use the fact that the longer side is 60' longer than with shorter side: Y = X + 60. Substitute this into the above equation to obtain:

 

2 * 5(X + 60) + 2(5X) + 100 = 900  --> 10(X + 60) + 2(5X) + 100 = 900  --> 10X + 600 + 10X + 100 = 900 

 

Combine like terms and solve...   20X + 700 = 900 --> 20X = 200  --> X = 10. Put the value of X into the equation 

Y = X + 60  --> Y = 70

 

Check answer in original equation: 2(5 * 70) + 2(5 * 10) + 100 = 900 True statement