I am assuming you do not mean The length of a triangle and you mean The length of a rectangle because the answer you given are the formula for the perimeter of a rectangle. With that said, the answer is D<span>.2w+2*(3w)112
The perimeter of a rectangle can be found by the following equation:
2L + 2W = P
OR
P = 2L + 2W
The equation </span>P = 2L + 2W is read perimeter = 2 times Length + 2 times width
The Question:
<span>The length of a rectangle is three times its width.if the perimeter is at its most 112 centimeters ,which is the greatest possible value of the the width.
</span>
The length of a rectangle
This means the perimeter
is
The word is means to use an equal sign
three times its width
This means 3 times w or 3w
The w = width
perimeter is at its most 112
This means <=
<= means less than or equal to
Ok so lets look at our equation
2L + 2W = P
2w + 2(3w) <= 112
Answer:40% weight increase
Step-by-step explanation:
(50-25)/2
25/2
12.5
25+12.5=37.5
Answer:
(5,1) is the mid point of RS
<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>
![x\approx 2.9ft](https://tex.z-dn.net/?f=x%5Capprox%202.9ft)
<h2>
Explanation:</h2><h2 />
First of all, let's calculate the area of the original rectangular garden:
![A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2](https://tex.z-dn.net/?f=A%3Db%5Ctimes%20h%20%5C%5C%20%5C%5C%20b%3Abase%20%5C%5C%20%5C%5C%20h%3Aheight%20%5C%5C%20%5C%5C%20%5C%5C%20b%3D12ft%20%5C%5C%20%5C%5C%20h%3D14ft%20%5C%5C%20%5C%5C%20%5C%5C%20A%3D12%2814%29%20%5C%5C%20%5C%5C%20A%3D168ft%5E2)
Jake wants to increase the area by 50%, so the new area would be:
![A'=168(1.5) \\ \\ A'=252ft^2](https://tex.z-dn.net/?f=A%27%3D168%281.5%29%20%5C%5C%20%5C%5C%20A%27%3D252ft%5E2)
He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:
![(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives](https://tex.z-dn.net/?f=%2812%2Bx%29%2814%2Bx%29%3D252%20%5C%5C%20%5C%5C%20168%2B12x%2B14x%2Bx%5E2-252%3D0%20%5C%5C%20%5C%5C%20x%5E2%2B26x-84%3D0%20%5C%5C%20%5C%5C%20%5C%5C%20Using%20%5C%20quadratic%20%5C%20formula%3A%20%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B-b%20%5Cpm%20%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D%20%5C%5C%20%5C%5C%20a%3D1%20%5C%5C%20%5C%5C%20b%3D26%20%5C%5C%20%5C%5C%20c%3D-84%20%5C%5C%20%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B-26%20%5Cpm%20%5Csqrt%7B26%5E2-4%281%29%28-84%29%7D%7D%7B2%281%29%7D%20%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B-26%20%5Cpm%20%5Csqrt%7B1012%7D%7D%7B2%7D%20%5C%5C%20%5C%5C%20%5C%5C%20Two%20%5C%20solutions%3A%20%5C%5C%20%5C%5C%20x_%7B1%7D%3D-13%2B%5Csqrt%7B253%7D%20%5Capprox%202.9%5C%5C%20%5C%5C%20x_%7B2%7D%3D-13-%5Csqrt%7B253%7D%20%5Capprox%20-28.9%20%5C%5C%20%5C%5C%20x_%7B2%7D%20%5C%20is%20%5C%20discarded%20%5C%20because%20%5C%20it%20%5C%20can%27t%20%5C%20be%20%5C%20negatives)
Finally:
<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>
![x\approx 2.9ft](https://tex.z-dn.net/?f=x%5Capprox%202.9ft)
<h2>Learn more:</h2>
Dilation: brainly.com/question/10945890
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