A rectangle has a perimeter of 24 inches. a new rectangle is formed with doubling the width and tripling the length. the new perimeter is 62 inches. what is the length and the w…

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asked Feb 10, 2024 80.9k views

2 Answers

Bumbu · Answer 1 · 2024-02-12T09:22:04+0000

Answer:

$Length=21in.\\Width=10in.$

Explanation:

consider the length of the original rectangle to be:
and the width of the original rectangle to be:
.

we can make 2 equations using these variables:

$2(x+y)=24 (originalperimeter)\\2(3x+2y)=62(newperimeter)$

from these 2 equations, we can simplify to get:

$x+y=12\\3x+2y=31$

we can multiply the first equation by
and add it to the second equation to find the value of x alone:

$-2x-2y=-24\\3x+2y=31\\3x-2x+2y-2y=31-24\\x=7$

now that we have the value of x, we can find the value of y:

$x+y=12\\7+y=12\\y=5$

and remember that the new rectangle has length 3x and width 2y, so:

3x=7*3=21 (length)

2y=2*5=10 (width)