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4 years ago

The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions

Mathematics

1 answer:

stiks02 [169]4 years ago

5 0

Answer:

width = 15 inches

length = 36 inches

Step-by-step explanation:

To solve you need to find the width...

width = w

length = 2w + 6

the perimeter is all the way around the area, so..

2w + 2(2w + 6) = 102

because there are 2 widths and 2 lengths in a perimeter.

Solve for w:

2w + 4w + 12 = 102

subtract 12 from both sides and combine like terms...

6w = 90

divide both sides by 6...

w = 15

the width = 15, and the length = 2(15) + 6 = 36

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1. Refer to the equation 2x - 4y = 12

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The coordinate pair can be obtained from the given equation by

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The table of values obtained from the given equation is presented as follows;

$\begin{array}{|c|cr|} \mathbf{x}&&\mathbf{y}\\0&&-3\\1&&-2.5\\2&&-2\\3&&-1.5\\4&&-1\end{array}\right]$

The graph showing the points in the above table is attached

Reason:

The given equation is presented as follows;

2·x - 4·y = 12

(a) The values are found by making either x, or y the subject of the

formula, and inputting values as follows;

2·x - 4·y = 12

= 4·y

4·y = 2·x - 12

$\dfrac{4\cdot y}{4} = \dfrac{2 \cdot x - 12}{4}$

The rearranged equation is therefore

$y = \dfrac{x }{2} - 3$

Plugging in values of x, (0, 1, 2, 3) to find the corresponding y-values gives;

x = 0

$y = \dfrac{0 }{2} - 3 = -3$

x = 1

$y = \dfrac{1 }{2} - 3 = -2 \dfrac{1 }{2}$

x = 2

$y = \dfrac{2 }{2} - 3 = -2$

x = 3

$y = \dfrac{3}{2} - 3 = -\dfrac{3}{2} = -1.5$

x = 4

$y = \dfrac{4}{2} - 3 = -1$

The table of values is therefore;

$\begin{array}{|c|cr|} \mathbf{x}&&\mathbf{y}\\0&&-3\\1&&-2.5\\2&&-2\\3&&-1.5\\4&&-1\end{array}\right]$

The graph of the points can be plotted using MS Excel as presented here

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The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions￼

The length of a rectangle is six more than double the width. If the perimeter is 102 inches find the dimensions