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3 years ago

The rectangle room is 2 times as long as it wide and its perimeter is 30 meters. Find the dimensions of the room.

1 answer:

4 0

Answer:
l = 10 m
w = 5 m

Steps:
Set equations:
l = 2w
30 = 2l + 2w

Substitute 2w with l in second equation to find l:
30 = 2l + 2w
30 = 2l + l
10 = l

Plug in 10 into first equation to find w:
l = 2w
10 = 2w
5 = w

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Answer:

Width = 17.5 feet,

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Step-by-step explanation:

We have been given that Darrin is hanging 200 feet of Christmas garland on the fencing that encloses his rectangular front yard. This means that perimeter of rectangular front yard is 200 feet.

We know that perimeter of rectangle is two times the sum of length and width of rectangle. We can represent this information in an equation as:

$2(l+w)=200...(1)$

We are also told that the length is 5 feet less than 5 times the width. We can represent this information in an equation as:

$l=5w-5...(2)$

Upon substituting equation (2) in equation (1), we will get:

$2(5w-5+w)=200$

$2(6w-5)=200$

$12w-10=200$

$12w-10+10=200+10$

$12w=210$

$\frac{12w}{12}=\frac{210}{12}$

$w=17.5$

Therefore, the width of rectangular front is 17.5 feet.

Upon substituting $w=17.5$ in equation (2), we will get:

$l=5(17.5)-5$

$l=87.5-5$

$l=82.5$

Therefore, the length of rectangular front is 82.5 feet.

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