A rug is shaped like a rectangle whose perimeter is 224ft. The length is 7 times as long as the width. Find the length and width.

badlife18va

badlife18va

Answered question

2022-08-03

A rug is shaped like a rectangle whose perimeter is 224ft. The length is 7 times as long as the width. Find the length and width.

Answer & Explanation

yassou1v

yassou1v

Beginner2022-08-04Added 14 answers

Step 1
Let x = length and   y = width
2 x + 2 y = 224 x + y = 112 x = 7 y
Substitute:
7 y + y = 112 8 y = 112 y = 112 8 y = 14   feet
Back-substitute
x = 7 ( 14 ) x = 98   feet
so, the length is 98 feet and the width is 14 feet.
Garrett Sheppard

Garrett Sheppard

Beginner2022-08-05Added 3 answers

Step 1
The length is 7 times longer than the width so, Length = 7x width or,
L = 7 w
perimeter is 224 ft so, the botder around the 4 sides is
L + w + L + w = 224
Using substitution:
Since L = 7 w
L + w + L + w = 224
is the same as
( 7 w ) + w + ( 7 w ) + w = 224
and
16 w = 224 w = 224 16 w = 14   feet
Find the length and width
Remember the length is 7w so
length = 98   feet
width = 14   feet
check figures:
perimeter is 224 ft
98 + 14 + 98 + 14 = ? = 224
yes

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