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Step2247 [10]
3 years ago
7

A rectangle has a length 6 more than it’s width if the width is decreased by 2 and the length decreased by 4 the resulting has a

n area of 21 square units what is the length of the original rectangle what is ratio of the original rectangle area to the new rectangle area what is the perimeter of the new rectangle
Mathematics
1 answer:
postnew [5]3 years ago
7 0

Length of original rectangle is : x+6 = 5+6 = 11 units

ratio of the original rectangle area to the new rectangle area:  \frac{55}{21}

perimeter of the new rectangle : 2(x+2+x-2) = 4x = 4(5) = 20 units

<u>Step-by-step explanation:</u>

Here we have , A rectangle has a length 6 more than it’s width if the width is decreased by 2 and the length decreased by 4 the resulting has an area of 21 square units what is the length of the original rectangle . We need to find what is ratio of the original rectangle area to the new rectangle area what is the perimeter of the new rectangle . Let's find out:

Initial parameters of rectangle are : Length = x+6 , width = x

width is decreased by 2 and the length decreased by 4  :

Length = x+6-4 = x+2 , width = x -2 , So area is :

⇒ Area = Length(width)

⇒ 21= (x+2)(x-2)

⇒ 21= x^2-4

⇒ x^2=25

⇒ x=5

So , Length of original rectangle is : x+6 = 5+6 = 11 units

ratio of the original rectangle area to the new rectangle area:

⇒ \frac{11(5)}{7(3)}

⇒ \frac{55}{21}

perimeter of the new rectangle : 2(x+2+x-2) = 4x = 4(5) = 20 units

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Step-by-step explanation:

Hey there! I will give the following steps, if you have any questions feel free to ask me in the comments below.

<u>Step 1:</u><u> </u><u><em>Remove parentheses.</em></u>

12 (2 − 2) + 32 = x + 6 + 2

<u>Step 2:</u><u> </u><u><em>Simplify 2 − 2 to 0.</em></u>

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<u>Step 3:</u><u> </u><u><em>Simplify 12 × 0 to 0.</em></u>

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