Question

The perimeter of a rectangular concrete slab is 114 feet and its area is 702 square feet. Find the dimensions of the rectangle.

A) Using l for the length of the rectangle, write an expression for the width of the rectangle in terms of l. (Hint: Solve the formula for w.) Show your work.

B) Write a quadratic equation using l, the expression you found in part (a), and the area of the slab.

C) Solve the quadratic equation. Use the two solutions to find the dimensions of the rectangle. PLz, Plz show work if you can. Thanks so much

Answer 1

@ganeshie8 @phi @mathstudent55 @zepdrix @Luigi0210

Answer 2

We know that:

Perimeter = 2L + 2W = 114...and
Area = LW = 702

As you said, were going to solve for W in terms of L for each equation:

2L + 2W = 114
2W = 114 - 2L
(2W/2) = (114/2) - (2L/2)
W = 57 - L

LW = 702
WL/L = 702/L
W = 702/L...Substitute 702/L for W in the equation: W = 57 - L

W = 57 - L
702/L = 57 - L...Cross-multiply
702 = -L^2 + 57L...Multiply each side of the equation by (-1)
-702 = L^2 - 57L
L^2 - 57L + 702 = 0

We have to factor this in order to find L. I used the Quadratic Formula where a = 1, b = -57, c = 702

The answers I got were L = 49, L = 18

To find which answer is correct out of the two, just substitute them into the equations that we created earlier. First, let's us L = 49

57 - L = W
57 - (49) = W
8 = W

702/L = W
702/49 = W
14.33 = W...As you can see, we have different values for W. Now let's try L = 18:

57 - L = W
57 - 18 = W
39 = W

702/L = W
702/18 = W
39 = W

Since W is the same for both equations, L = 18 would be the correct answer out of the two

FINAL ANSWER: The W of the rectangle is 39 and the L of the rectangle is 18