Mathematics, 25.01.2020 12:31 naomihiggins4033

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?

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Answer from: Tuxkie

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

P = 2l + 2w

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

According to the statement we have to:

$l = w + 3 \frac {1} {6} = w + \frac {19} {6}\\P = 15 \frac {1} {3} = \frac {46} {3}$

The length and perimeter are expressed in centimeters.

Substituting we have:

$\frac {46} {3} = 2 (w + \frac {19} {6}) + 2w\\\frac {46} {3} = 2w + \frac {38} {6} + 2w\\\frac {46} {3} = 2w + \frac {19} {3} + 2w\\\frac {46} {3} = 4w + \frac {19} {3}\\\frac {46} {3} - \frac {19} {3} = 4w\\\frac {27} {3} = 4w\\$

$9 = 4w\\w = \frac {9} {4}$

Thus, the width of the rectangle is $\frac {9} {4}$ centimeters.

The length is:

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

$l=\frac{65}{12}$ centimeters

$w=\frac{9}{4}$ centimeters

Answer from: jaidalynkimora

The length of the triangle is $\frac{65}{12} cm$ and the width is $\frac{9}{4} cm$

Step-by-step explanation:

Given

Length of the Rectangle = $3\frac{1}{6}$ longer than the width

Perimeter of the Rectangle = $15\frac{1}{3}$

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 = $3\frac{1}{6}$ + W

P = $15\frac{1}{3}$

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

So,

P = 2( L + W) becomes

$15\frac{1}{3} = 2(3\frac{1}{6} + W + W)$

$15\frac{1}{3} = 2(3\frac{1}{6} + 2W)$

Convert fractions to improper fractions

$\frac{46}{3} = 2(\frac{19}{6} + 2W)$

Open Bracket

$\frac{46}{3} = 2 * \frac{19}{6} + 2 * 2W$

$\frac{46}{3} = \frac{19}{3} + 4W$

Make 4W the subject of of formula

$4W = \frac{46}{3} - \frac{19}{3}$

$4W = \frac{46 - 19}{3}$

$4W = \frac{27}{3}$

4W = 9

Make W the subject of of formula

$W = \frac{9}{4}$

Recall that

L = $3\frac{1}{6}$ + W

So, $L = 3\frac{1}{6} + \frac{9}{4}$

$L = \frac{19}{6} + \frac{9}{4}$

$L = \frac{38 + 27}{12}$

$L = \frac{65}{12}$

Hence, the length of the triangle is $\frac{65}{12} cm$ and the width is $\frac{9}{4} cm$

Answer from: Quest

c. 27 units.

step-by-step explanation:

we are told that in circle a, ∠bae ≅ ∠dae.

we can see from our given diagram that in $\delta bea$ and $\delta dea$ ;

$ba=da$ , as these are radii of our given circle.

$ea=ea$

therefore, $\delta bea\cong \delta dea$ by sas congruence postulate.

hence, side be will be equal to side de as corresponding parts of congruent triangles are congruent. so we can set an equation to find the value of x as:

$3x-24=x+10$

$3x-x=24+10$

$2x=34$

$x=\frac{34}{2}$

$x=17$

now let us substitute x=17 in the expression for the length of be.

$\text{length of be}=3x-24$

$\text{length of be}=3\cdot 17-24$

$\text{length of be}=51-24$

$\text{length of be}=27$

therefore, length of be will be 27 units and option c is the correct choice.

In circle a, ∠bae ≅ ∠dae. what is the length of be? 14 units 17 units 27 units 34 units

Answer from: Quest

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}

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