Question

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

a. Using l for the length of the rectangle, write an expression for the width of the rectangle in terms of l.
P = 2l+ 2w
114 = 2l + 2w
114 - 2l = 2w
Then Divide by 2: 57 - l = w
b. Write a quadratic equation using l, the expression you found in part (a), and the area of the slab.
l ( 57 - l) = 702
57l - l^2 = 702
l^2 - 57l = -702
l^2 - 57l + 702 = 0
c. Solve the quadratic equation. Use the two solutions to find the dimensions of the rectangle.
I don't know how to do c. Help please.

Answer 1

to solve quadratic equation of the form
\[ax ^{2}+bx+c=0\]
you can use this formula:
\[x=\frac{ -b \pm \sqrt{b ^{2}-4ac} }{ 2a }\]
here, you have the equation of variable l in it.
so you can compare your equation by\[al ^{2}+bl+c=0\]
and solve for l.