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vlabodo [156]
4 years ago
13

A rectangular deck has a perimeter of 126 feet and an area of 972 square feet. What are the dimensions of the deck?

Mathematics
1 answer:
Natasha_Volkova [10]4 years ago
4 0

Answer:

27 ft x 36 ft

Step-by-step explanation:

2 (L + W) = 126

L + W = 63

LW = 972

L ( 63 - L) = 972

63L - L² = 972

L² - 63L + 972 = 0

(L-27) (L - 36) = 0

L = 27 or L = 36

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x = \frac{ 419 }{ 113 } ~,~y = -\frac{ 208 }{ 113 } ~,~z = \frac{ 21 }{ 113 }

<h2>Explanation:</h2>

We have the following system of three linear equations:

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Let's use elimination method in order to get the solution of this system of equation, so let's solve this step by step.

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\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\4~ x&+~~5~ y&+~~2~ z&~=~6\end{array}

Step 2: Multiply first equation by −2 and add the result to the third equation. So we get:

\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&-~~~3~ y&-~~~62~ z&~=~-6\end{array}

Step 3: Multiply second equation by −32 and add the result to the third equation. So we get:

\begin{array}{ cccc }2~ x&+~~4~ y&+~~32~ z&~=~6\\&-~~~2~ y&-~~~79~ z&~=~-11\\&&+~~\frac{ 113 }{ 2 }~ z&~=~\frac{ 21 }{ 2 }\end{array}

Step 4: solve for z.

\begin{aligned}       \frac{ 113 }{ 2 } ~ z & = \frac{ 21 }{ 2 } \\      z & = \frac{ 21 }{ 113 }       \end{aligned}

Step 5: solve for y.

\begin{aligned}-2y-79z &= -11\\-2y-79\cdot \frac{ 21 }{ 113 } &= -11\\y &= -\frac{ 208 }{ 113 } \end{aligned}

Step 6: solve for x by substituting y=-\frac{208}{113} and z = \frac{21}{113} into the first equation:

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Finally:

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<h2>Learn more:</h2>

Solving System of Equations: brainly.com/question/13121177

#LearnWithBrainly

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