A. Find The Value Of X. B. Find The Length Of Of The Banner. C. Find The Width Of…

a. Find the value of x.

b. Find the length of of the banner.

c. Find the width of the banner.

d. Find the perimeter of the banner.

Answer:

[tex]\tt a.) \ 13\\b.) \ 120 \ in\\c.) \ 80 \ in\\d.) \ 400 \ in[/tex]

Solution:

a. Find the value of x.

The shape of a banner is a rectangle so we need to apply the basics of rectangles in order to answer this.

[tex]\tt \overline{ GE} = \overline{MO}[/tex]

[tex]\tt 9x +3 = 15x-75[/tex]

[tex]\tt 75 +3 = 15x-9x[/tex]

[tex]\tt 78 = 6x[/tex]

[tex]\tt 6x = 78[/tex]

[tex]\tt \dfrac{6x}{6}=\dfrac{78}{6}[/tex]

[tex]\tt \boxed{x=13}[/tex]

b. Find the length of of the banner.

The length of the banner is either the measure of [tex]\tt \overline {GE}[/tex] or [tex]\tt \overline {MO}[/tex]. You can choose one. I’ll be using [tex]\tt \overline {GE}[/tex].

[tex]\tt \overline {MO} = 9x+3\\\tt \overline {MO} = 9(13)+3\\\tt \overline {MO} =117+3\\\tt \overline {MO} =120 \ in[/tex]

Therefore, the length of the banner is [tex]\large \boldsymbol {\tt 120 \ in}[/tex].

c. Find the width of the banner.

The width of the banner is the measure of [tex]\tt \overline {GM}[/tex].

[tex]\tt \overline {GM} = 5x+15[/tex]

[tex]\tt \overline {GM} = 5(13)+15[/tex]

[tex]\tt \overline {GM} = 65+15[/tex]

[tex]\tt \overline {GM} = 80 \ in[/tex]

Therefore, the width of the banner is [tex]\large \boldsymbol {\tt 80 \ in}[/tex].

d. Find the perimeter of the banner.

The perimeter of the rectangle is the sum of the measure of the sides.

We can use the formula: [tex]\tt P=2 \ ( \ Length \ + \ Width \ )[/tex]

[tex]\tt P=2 \ ( \ 120 \ + \ 80\ )[/tex]

[tex]\tt P=2 \ ( 200 )[/tex]

[tex]\tt P=400[/tex]

So, we have our perimeter which measures [tex]\large \boldsymbol {\tt 400 \ in}[/tex].

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