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.

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

Let the perimeter = p
Let the width = w
We are given that the length = l
p=(2 * l) + (2 * w)
p = 2l + 2w ................(1)
Can you rearrange equation (1) to find l = ???????????

Answer 2

Sorry. I should have asked you to rearrange equation (1) to find w = ????????

Answer 3

2w=p(2*l)

Answer 4

p = 2l + 2w
Subtracting 2l from both sides gives
2w = p -2l
Dividing both sides by 2 gives
\[w=\frac{p-2l}{2}\ .................(2)\]
The next step is to substitute the given value for p into equation (2). Can you do that?

Answer 5

@newbold_galen Are you there?

Answer 6

sorry hadto put baby brother to bed for nap

Answer 7

OK :)

Answer 8

\[w=\frac{ 114-2l }{ 2 }\]

Answer 9

Correct! And dividing each term in the numerator by 2 we get
w = 57 - l ................(3)
Area = l * w = l(57 - l)
\[702=l(57-l)\ ...............(4)\]
Can you form equation (4) into a quadtratic?

Answer 10

quadratic*

Answer 11

nope. quadratic equations lose me everytime

Answer 12

\[702=l(57-l)\ ...............(4)\]
First multiply out the right hand side. Can you do that?

Answer 13

no

Answer 14

\[l(57-l)=57l-l ^{2}\]
So we now have
\[702=57l-l ^{2}\ .................(5)\]
If you add l^2 to both sides of equation (5) and subtract 57l from both sides, the right hand side will become zero and you will have formed a quadratic equation. Can you try that?

Answer 15

The quadratic is
\[l ^{2}-57l+702=0\]

Answer 16

\[l ^{2}-57l+\]

Answer 17

702=0

Answer 18

To solve this quadratic use the formula that will solve any quadratic
\[\frac{-b \pm \sqrt{(b ^{2}-4ac)}}{2a}\]
In your question b = -57, a = 1 and c = 702. Just substitute into the formula.