<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>

$x\approx 2.9ft$

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

$A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2$

Jake wants to increase the area by 50%, so the new area would be:

$A'=168(1.5) \\ \\ A'=252ft^2$

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:

$(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives$

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>

$x\approx 2.9ft$

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

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6 0

3 years ago

Please help, trigonometry is hard for me

Vsevolod [243]

Because the cos theta < 0 then theta must be an obtuse angle

so a^2 + b^2 < a^2

6 0

3 years ago

PLLEASE ANSWER THIS FOR ME

stiv31 [10]

Answer:

<h2>120 square meters</h2>

Step-by-step explanation:

To find the SA of 2 Triangles, we will use the formula... B x H, and the Base and Height is going to be the dimensions of just 1 triangle, but it's going to give the answer for 2 triangles, in this shape, we have 2 triangles.

SA = B x H

= 6 x 4

= 24

24 square meters for both of the triangles

Now, let's find the SA of the rectangle on the bottom...

SA = L x W

= 6 x 6

= 36

36 square meters for 1 of the 3 rectangular parts, the one on the bottom

Now, lets find the SA of the 2 rectangles on the top. We'll use the dimensions of 1 rectangle and find the answer for 2 answers by using the formula...

SA = L x W x 2

= 6 x 5 x 2

= 30 x 2

= 60

60 square meters for the 2 rectangles on the top.

Now, we have to add all of our answers.

24 + 36 + 60 = 120 square meters

<h2>Hence, the SA (surface area) of this shape is 120 square meters.</h2>

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4 0

2 years ago