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

deja vu
we have 2 equations, 1 for perimeter and 1 for area, both in terms of l&w
P=2L+2W
A=LW

We know P and A
2L+2W=114
LW=702

Let's solve for W in terms of L in the perimeter equation:
2L+2W=114
L+W=57
W=57-L

Now let's substitute this value into the area equation:
LW=702
L(57-L)=702
57L-L^2=702
L^2-57L+702=0
factor this into:
(L-18)(L-39)=0
L=18, 39

Now we have the possible lengths: 18 and 39
If the length is 39, the width is 702/39=18 because LW=702
39W=702
W=18
If the length is 18, the width is 702/18=39
So the dimensions of the rectangle are 39 ft X 18 ft
You can check this by plugging these values back into the perimeter and area equations:
LW=702
(18)(39)=702? true, this works
2(18)+2(39)=114?
36+78=114?
114=114? true

Answer 2

thanks, so much

Answer 3

yw