ryanh0342
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The length of a rectangle is 3 (1)/(6) cm longer than the width. The perimeter of the rectangle is 15 (1)/(3) cm. What are the width and length of this rectangle?

Respuesta :

carlosego

For this case we have that by definition, the perimeter of a rectangle is given by:

[tex]P = 2l + 2w[/tex]

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

According to the statement we have to:

[tex]l = w + 3 \frac {1} {6} = w + \frac {19} {6}\\P = 15 \frac {1} {3} = \frac {46} {3}[/tex]

The length and perimeter are expressed in centimeters.

Substituting we have:

[tex]\frac {46} {3} = 2 (w + \frac {19} {6}) + 2w\\\frac {46} {3} = 2w + \frac {38} {6} + 2w\\\frac {46} {3} = 2w + \frac {19} {3} + 2w\\\frac {46} {3} = 4w + \frac {19} {3}\\\frac {46} {3} - \frac {19} {3} = 4w\\\frac {27} {3} = 4w\\[/tex]

[tex]9 = 4w\\w = \frac {9} {4}[/tex]

Thus, the width of the rectangle is [tex]\frac {9} {4}[/tex] centimeters.

The length is:

[tex]l = w + \frac {19} {6} = \frac {9} {4} + \frac {19} {6} = \frac {54 + 76} {24} = \frac {130} {24} = \frac {65} {12}[/tex] centimeters.

Answer:

[tex]l=\frac{65}{12}[/tex] centimeters

[tex]w=\frac{9}{4}[/tex] centimeters

MrRoyal

Answer:

The length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

Step-by-step explanation:

Given

Length of the Rectangle = [tex]3\frac{1}{6}[/tex] longer than the width

Perimeter of the Rectangle = [tex]15\frac{1}{3}[/tex]

Required

What are the width and length of the rectangle.

Let L represent the length of the rectangle, W represent the width of the rectangle and P represent the Perimeter.

So, we have that

L = [tex]3\frac{1}{6}[/tex] + W

P = [tex]15\frac{1}{3}[/tex]

Perimeter of a rectangle is calculated by 2( L + W)

So,

P = 2( L + W) becomes

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + W + W)[/tex]

[tex]15\frac{1}{3} = 2(3\frac{1}{6} + 2W)[/tex]

Convert fractions to improper fractions

[tex]\frac{46}{3} = 2(\frac{19}{6} + 2W)[/tex]

Open Bracket

[tex]\frac{46}{3} = 2 * \frac{19}{6} + 2 * 2W[/tex]

[tex]\frac{46}{3} = \frac{19}{3} + 4W[/tex]

Make 4W the subject of of formula

[tex]4W = \frac{46}{3} - \frac{19}{3}[/tex]

[tex]4W = \frac{46 - 19}{3}[/tex]

[tex]4W = \frac{27}{3}[/tex]

[tex]4W = 9[/tex]

Make W the subject of of formula

[tex]W = \frac{9}{4}[/tex]

Recall that

L = [tex]3\frac{1}{6}[/tex] + W

So, [tex]L = 3\frac{1}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{19}{6} + \frac{9}{4}[/tex]

[tex]L = \frac{38 + 27}{12}[/tex]

[tex]L = \frac{65}{12}[/tex]

Hence, the length of the triangle is [tex]\frac{65}{12} cm[/tex] and the width is [tex]\frac{9}{4} cm[/tex]

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