Respuesta :
The answer is: The length of the original rectangle is 24 meters.
Explanation:
1. The perimeter of a rectangle is:
[tex]P=2L+2W[/tex]
Where [tex]L[/tex] is the length and [tex]W[/tex] is the width
2. The perimeter of the original rectangle is 88 meters, therefore:
[tex]88=2L+2W[/tex] (First equation)
3. The width were doubled, the length were increased by 12 meters and the new perimeter is 152 meters. Therefore:
[tex]152=2(L+12)+2(2W)[/tex]
[tex]128=2L+4W[/tex] (Second equation)
4. As you can see, you have a system of equations:
[tex]\left \{ {{2L+2W=88} \atop2L+4W=128}} \right.[/tex]
5. You can solve it by applying the Elimination Method. Multiply the first equation by -1, add both equations and solve for [tex]W[/tex]:
[tex]\left \{ {{-2L-2W=-88} \atop2L+4W=128}} \right.[/tex]
[tex]2W=40\\W=20[/tex]
6. Now, you can calculate the lenght by substituying the width into one of the original equations:
[tex]2L+2(20)=88\\2L=48\\L=24[/tex]
The original length of the rectangle is [tex]\boxed{24{\text{ m}}}[/tex] and the width of the rectangle is [tex]\boxed{20{\text{ m}}}.[/tex]
Further explanation:
The perimeter the rectangles can be obtained as follows,
[tex]\boxed{{\text{Perimeter}} = 2l + 2w}[/tex]
Here, [tex]\text{l}[/tex] is the length and [tex]\text{w}[/tex] is the width.
Given:
The original perimeter of the rectangle is [tex]88{\text{ m}}.[/tex]
The increased perimeter of the rectangle is [tex]152{\text{ m}}.[/tex]
Explanation:
Consider the original length of the rectangle as [tex]\text{x}[/tex].
Consider the original width of the rectangle as [tex]\text{y}[/tex].
The original perimeter of the rectangle is [tex]88{\text{ m}}.[/tex]
[tex]\begin{aligned}2\left({x + y} \right) &= 88\\x + y &= \frac{{88}}{2}\\x + y &= 44\\x &= 44 - y\\\end{aligned}[/tex]
The length is increased by 12 and the width is double.
[tex]\begin{aligned}2\left( {x + 12 + 2y} \right) &= 152\\x + 12 + 2y &= \frac{{152}}{2}\\x + 2y &= 76 - 12\\x + 2y &= 64\\\end{aligned}[/tex]
Substitute [tex]44 - y[/tex] for [tex]\text{x}[/tex]
[tex]\begin{aligned}44 - y + 2y&= 64\\y&= 64 - 44\\y&= 20\\\end{aligned}[/tex]
The length can be obtained as follows,
[tex]\begin{aligned}x&= 44 - 20\\x&= 24\\\end{aligned}[/tex]
The original length of the rectangle is \boxed{24{\text{ m}}} and the width of the rectangle is [tex]\boxed{20{\text{ m}}}.[/tex]
Learn more:
- Learn more about inverse of the functionhttps://brainly.com/question/1632445.
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Answer details:
Grade: High School
Subject: Mathematics
Chapter: Rectangle
Keywords: 88 m, width, doubled, length, increases by 12, original rectangle, rectangles, perimeter, number of rectangles, 2 rectangles, 3 rectangles, table, between the sides, represents.
