Number 3 it's algebraic expressions

the length of a rectagle is 5 in longer than its width. if the perimeter of the rectangle is 58 in, find its length and width

dolphi86 [110]

Answer:

Length = 17 inches

Width = 12 inches

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Step-by-step explanation:

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As it is given that, the length of a rectangle is 5 in longer than its width and the perimeter of the rectangle is 58 in and we are to find the length and width of the rectangle. So,

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Let us assume the width of the rectangle as x inches and therefore, the length will be (x + 5) inches .

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Now, <u>According to the Question :</u>

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${\longrightarrow \qquad { \pmb{\frak {2 ( Length + Breadth )= Perimeter_{(Rectangle)} }}}}$

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${\longrightarrow \qquad { {\sf{2 ( x + 5 + x )= 58 }}}}$

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${\longrightarrow \qquad { {\sf{2 ( 2x + 5 )= 58 }}}}$

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${\longrightarrow \qquad { {\sf{ 4x + 10= 58 }}}}$

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${\longrightarrow \qquad { {\sf{ 4x = 58 - 10}}}}$

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${\longrightarrow \qquad { {\sf{ 4x = 48}}}}$

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${\longrightarrow \qquad { {\sf{ x = \dfrac{48}{4} }}}}$

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${\longrightarrow \qquad{ \underline{ \boxed { \pmb{\mathfrak {x = 12}} }}} }\: \: \bigstar$

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Therefore,

The width of the rectangle is 12 inches .

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Now, We are to find the length of the rectangle:

${\longrightarrow \qquad{ { \frak{\pmb{Length = x + 5 }}}}}$

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${\longrightarrow \qquad{ { \frak{\pmb{Length = 12 + 5 }}}}}$

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${\longrightarrow \qquad{ { \frak{\pmb{Length = 17}}}}}$

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Therefore,

The length of the rectangle is 17 inches .

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8 0

1 year ago

Read 2 more answers

Which ratio is equivalent to 7:3?

aliina [53]

Answer:

The answer is B.

Step-by-step explanation:

7x4 is 28 which means you have to multiply 3x4. That gives you 12. 28:12 is the proper ratio. (Hope this helped!)

3 0

2 years ago

Read 2 more answers

HELP!<br> -1/4 × (-7/9)

boyakko [2]

Answer:

7

I hope this is helps.

7 0

3 years ago

Need help ASAP <br> questions in the pics i have sent

Cloud [144]

Answer:

Step-by-step explanation:

Picture 1

In right triangle ABC,

Side AB is the opposite side of angle C.

Picture 2

In triangle MKL,

tan(∠M) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

= $\frac{KL}{KM}$

= $\frac{15}{8}$

Option (1) is the answer.

Picture 3

In ΔXYZ,

sin(∠Z) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

= $\frac{XY}{XZ}$

For the length of XY we will apply Pythagoras theorem in ΔXYZ,

XZ² = XY² + YZ²

XY² = XZ² - YZ²

= (40)² - (32)²

XY = √576

= 24

sin(Z) = $\frac{24}{40}$

sin(Z) = $\frac{3}{5}$

Picture 4

In right triangle DEF,

Cos(D) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

= $\frac{EF}{DF}$

= $\frac{75}{72}$

= $\frac{25}{24}$

Picture 5

In ΔABC,

tan(63°) = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

tan(63°) = $\frac{BC}{AB}$

AB = $\frac{BC}{\text{tan}(63)}$

AB = $\frac{8}{\text{tan}(63)}$

AB = 4.0762 ≈ 4 m

Option (3) will be the answer.

7 0

3 years ago

Write a linear equation that passes through the two points (-6, -7) and (3, -4).

Phantasy [73]

linear equation that passes through the two points (-6, -7) and (3, -4) is $y=\frac{1}{3}x-5$

Step-by-step explanation:

We need to write the equation that passes through the two points (-6, -7) and (3, -4).

The equation can be written is point slope form.

The standard form of point slope equation is:

$y=mx+b$

where m is the slope and b is the y-intercept

Finding slope m:

Slope can be found by using formula:

$slope = \frac{y_{2}-y_{1}}{x{2}-x_{1}} \\Where\,\, y_{2}=-4,y_{1}=-7,x{2}=3,x_{1}=-6\\slope =\frac{-4-(-7)}{3-(-6)}\\slope=\frac{-4+7}{3+6}\\slope=\frac{3}{9}\\slope=\frac{1}{3}$