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:**

**Answer:**

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

**Solution:**

**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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