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A rectangle has a length that is 7 less than 4 times the width. The perimeter is 100 in. Find the length and the width.

User Deelux
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1 Answer

21 votes
21 votes

Answer:

136 m

Explanation:

Let w = the width of the rectangular field.

Let l = the length of the rectangular field.

The formula for the perimeter P of the rectangular field is:

P = 2w + 2l

Since the length l is 7 m less than 4 times the width w, then we can write the following equation that relates l and w:

l = 4w - 7 m

Since l = 4w - 7 and it's given that perimeter P = 136 m, then we can substitute this information into the perimeter formula as follows:

P = 2w + 2l

136 m = 2w + 2(4w - 7 m)

136 m = 2w + 2(4w) - 2(7 m)

136 m = 2w + 8w - 14 m

136 m + 14m = 10w - 14 m + 14 m

150 m = 10w + 0

10w = 150 m

(10w)/10 = 150 m/10

(10/10)w = 150 m/10

(1)w = 15 m

w = 15 m

Therefore, l = 4w - 7 m

l = 4(15 m) - 7 m

l = 60 m - 7m

l = 53 m

CHECK:

P = 2w + 2l

136 m = 2(15 m) + 2(53 m)

136 m = 30 m + 106 m

136 m = 136 m

User Henrik H
by
3.2k points