The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

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The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

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Answer 1 · 2015-12-21T15:50:32

length $= 10.5$ $=10.5$ $c m$ $cm$
width $= 7.5$ $=7.5$ $c m$ $cm$

Explanation:

Start by making let statements to represent variables as the length and width as stated in the question.

Let $4 x$ $4x$ represent the width.
Let $4 x + 3$ $4x+3$ represent the length.

$2 [(4 x) + (4 x + 3)] = 36$ $2[(4x)+(4x+3)]=36$
$2 [8 x + 3] = 36$ $2[8x+3]=36$
$8 x + 3 = 18$ $8x+3=18$
$8 x = 15$ $8x=15$
$x = \frac{15}{8}$ $x=15/8$

To find the dimensions, substitute $x = \frac{15}{8}$ $x=15/8$ into $4 x$ $4x$ (width) and $4 x + 3$ $4x+3$ (length).

Finding the width

$w = 4 x$ $w=4x$

$w = 4 (\frac{15}{8})$ $w=4(15/8)$

$w=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)$

$w=15/2$

$w=7.5$

Finding the length

$l=4x+3$

$l=4(15/8)+3$

$l=color(red)cancelcolor(black)4(15/color(red)cancelcolor(black)8^2)+3$

$l=15/2+3$

$l=21/2$

$l=10.5$

$:.$ , the length is $10.5$ $cm$ and the width is $7.5$ $cm$ .

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The length of a rectangle is 3 cm more than four times the width. If the perimeter of the rectangle is 36 cm, what are its dimemions?

1 Answer

Explanation:

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