the perimeter of a rectangular concrete slab is 106 feet and its area is 570 sqaure feet. what is the length of the longer side of the slab?
Can you show your work too. Thanks <3
Can you show your work too. Thanks <3
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Let x = length of slab and y = width of slab. Then the perimeter P = 2x + 2y and
the area A = xy. We are given that P = 106 feet and A = 570 feet^2, so
2x + 2y = 106 ----> x + y = 53 ---> y = 53 - x. Now substitute this expression for y
into the area equation to get A = x*y = x*(53 - x) = 570 ---> 53x - x^2 = 570 --->
x^2 - 53x + 570 = 0. Now use the quadratic equation to solve for x:
x = (53 +/- sqrt((-53)^2 - 4*1*570)) / 2 = (53 +/- sqrt(529))/2 = (53 +/- 23)/2,
so either x = (53 + 23)/2 = 38 feet or x = (53 - 23)/2 = 15 feet.
If x = 38 feet then y = 53 - 38 = 15 feet, and if x = 15 feet then y = 53 - 15 = 38 feet.
So either way the slab has dimensions 15 feet by 38 feet.
Note that 15 * 38 = 570, so the product of these dimensions is the desired area of
the slab, thus confirming the solution.
the area A = xy. We are given that P = 106 feet and A = 570 feet^2, so
2x + 2y = 106 ----> x + y = 53 ---> y = 53 - x. Now substitute this expression for y
into the area equation to get A = x*y = x*(53 - x) = 570 ---> 53x - x^2 = 570 --->
x^2 - 53x + 570 = 0. Now use the quadratic equation to solve for x:
x = (53 +/- sqrt((-53)^2 - 4*1*570)) / 2 = (53 +/- sqrt(529))/2 = (53 +/- 23)/2,
so either x = (53 + 23)/2 = 38 feet or x = (53 - 23)/2 = 15 feet.
If x = 38 feet then y = 53 - 38 = 15 feet, and if x = 15 feet then y = 53 - 15 = 38 feet.
So either way the slab has dimensions 15 feet by 38 feet.
Note that 15 * 38 = 570, so the product of these dimensions is the desired area of
the slab, thus confirming the solution.