Question

The perimeter of a rectangle parking lot is 146 meters find the dimension of the lot if the length is 7 meters less than 4 times the width

Answer 1

The dimensions of the rectangle parking lot with a perimeter of 146 meters and length 7 meters less than 4 times the width are 57 meters in length and 16 meters in width.

Step-by-step explanation:

To find the dimensions of a rectangle where the perimeter is 146 meters and the length is 7 meters less than 4 times the width, we can set up the following equations:

Let w be the width of the parking lot. Then, the length l can be represented as l = 4w - 7.

The perimeter of a rectangle is given by the formula P = 2l + 2w. Given that the perimeter P is 146 meters, we can substitute the expressions for l and w into the perimeter formula to get 146 = 2(4w - 7) + 2w.

Simplifying, we have:

146 = 8w - 14 + 2w

1. 146 = 10w - 14
2. 146 + 14 = 10w
3. 160 = 10w
4. w = 16

Now that we have the width, we can find the length:

1. l = 4w - 7
2. l = 4(16) - 7
3. l = 64 - 7
4. l = 57

Therefore, the dimensions of the parking lot are 57 meters in length and 16 meters in width.

Answer 2

146=2(l)+2(w) Let 4w-7=l
146=2(4w-7)+2w
146=10w-14 Add 14 to both sides
160=10w Divide by 10
16=Width Plug width back into the formula
57=Length