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.

Answer 1

a) perimeter
2L + 2w = 114
2w = 114 - 2L
w = 57 - L


b) for the area
Lw = 702
L(57 - L) = 702
57L - L² = 702
L² - 57L + 702 =0

c) quadratic equations
L = (57 ±√(-57² - 4(1)(702))) / (2(1))
L = 39
L = 18

the rectangle is 18 by 39 feet

we could have factored the equation to solve as well
L² - 57L + 702 =0
(L - 18)(L - 39) = 0

L = 18 or L = 39