I take a test tomorrow and I doing practice problems.?

Question

How do I set up this problem:

The width of a rectangula parking lot is 10 feet longer than three fifths of the length. The perimeter of the lot is 500 feet. Find the area of the parking lot.

Thanks!

Answer 1

Use a couple variables to represent length and width.
Let L = length
Let W = width

"The width" --> W
"is" --> =
"10 feet longer than" --> 10 +
"three-fifths the length" ---> (3/5)L

So now you have a way to represent W in terms of L:
W = 10 + 3/5L

The perimeter is the sum of the sides of the rectangle. You add the width twice and the length twice. Thus the formula for the perimeter is:

Perimeter = 2(L + W)

Substitute in W = 10 + (3/5)L:

Perimeter = 2(L + (3/5)L + 10)

And you are given that the perimeter is 500 ft.:
500 = 2(L + (3/5)L + 10)

Divide both sides by 2:
250 = L + (3/5)L + 10

Subtract 10 from both sides:
240 = L + (3/5)L

Distribute out an L:
240 = (1 + 3/5)L

Simplify:
240 = (8/5)L

Multiply both sides by 5/8:
(5/8)240 = L

Simplify:
L = (240/8) * 5
L = 30 * 5
L = 150 ft.

Now plug this into W = 10 + (3/5)L, to get a value for W:
W = 10 + (3/5)(150)
W = 10 + 3 * (150/5)
W = 10 + 3 * 30
W = 10 + 90
W = 100 ft.

As a double check, confirm that the perimeter is 500 ft. (100 + 150 + 100 + 150 = 500 ft.)

Now just figure the area:
Area = L x W
Area = 150 x 100
Area = 15,000 sq. ft.

Answer 2

Start with the first sentance.

The width is 10 feet longer than 3/5 the length. Change that to an equation

W = 10 + 3/5*L, where W is width and L is length.

"Is" in a sentance always means equal. Longer in this instance means add. Three fifths the length means multiply 3/5 by the length.

Take the next sentance and make it into an equation. The equation for perimeter is 2W + 2L = perimeter. So:

2W + 2L = 500 feet, where W is width and L is length again.

The area of a rectangle is L*W. Use the frist 2 equations to solve for L and W. Then use L and W to find the area.

Answer 3

ok. we know that to find the aream we need the length x the breath

( 3/5x + 5/5x + 10 feet ) x 2 = 500 feet.


( 3/5x + 5/5x + 10 feet ) = 250 feet

3/5x + 5/5x = 250 - 10 feet = 240 feet

240 / 8 = 30 feet


so the length is 30 feet multifly by 5 = 150 feet

and the breath is 30 feet multiply by 3 + 10 feet = 90 + 10 = 100 feet



to check . take the length multifplt by 2 + the breath multiply by 2

= 150 x 2 + 100 x 2
= 300 + 200
= 500

hence we are correct.



so , we now know the length and breath , to find the area, we simply multiply the length and breath ,

150 x 100 = 15000 feet squared


hope this helps


so what you do is find out the individual lengths by looking at how many parts the perimeter is divided by

all the best !

Answer 4

The width of a rectangula parking lot is 10 feet longer than three fifths of the length.

1) W = 10 + 3L/5

The perimeter of the lot is 500 feet

2) 2W + 2L = 500

Since equation 1 is already solved for W in terms of L, substitute this into equation 2

2(10 + 3L/5) + 2L = 500

Solve this for L and get W from equation `

I get L = 150, W = 100

Answer 5

perimeter of a rectangle: p = 2(L + w)=500
area of a triangle: a = L * w
w = 10 + 3/5L

so 2(L + 10 + 3/5L)=500
8/5L = 250 - 10 = 240
L = 240*5/8 = 150
w = 10 + 3/5 *150 = 100
so the area will be a=150*100=15 000

Answer 6

The first sentence says:
W = 10 + (3/5)L. (i)
The second says:
P = 2L + 2W = 500. (ii)

Since A =LW, you need to find L & W, using (i) & (ii).

[Remember the units.]

Answer 7

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