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arlik [135]
3 years ago
15

Can someone answer by EXPLAINING the question detailed please I am trying to get it

Mathematics
1 answer:
lidiya [134]3 years ago
3 0
I am assuming you were supposed to be using Pythagorean theorem. So I will help you solve it that way. As you know Pythagorean theorem needs a right angle and the three sites.Because the line is a tangential wine that means that it is perpendicular to a radius; therefore, that’s the right angle. r and 120 are legs, a & b. The hypotenuse is 80 plus what? How long? 80+ r.
Pythagorean Theorem:
A^2 + b^2 = c^2
120^2 + r^2 = (80 + r)^2
(120)(120) + r^2 = (r + 80)(r +80))
14400+ r^2 = r^2 + 160r + 6400
8000=160r
R=5 ft.
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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

⠀

Step-by-step explanation:

⠀

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,

⠀

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

⠀

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

⠀

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

⠀

{\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 }}}}

⠀

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

⠀

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

⠀

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

⠀

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

⠀

Therefore,

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⠀

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

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

⠀

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

⠀

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

⠀

Therefore,

  • The length of the rectangle is 17 inches .

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