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Answer :
Let's solve the problem step-by-step.
a. Write an equation for the perimeter:
The problem states that the pentagon's perimeter is the sum of its side lengths, which equals 45 centimeters. In this case, the sides are given as three sides of length [tex]\( x \)[/tex] and two sides of length [tex]\( 3x \)[/tex]. So, we can write the equation for the perimeter as:
[tex]\[ x + x + x + 3x + 3x = 45 \][/tex]
b. Solve the equation:
Let's simplify the equation:
[tex]\[ 3x + 6x = 45 \][/tex]
When simplified, this equation becomes:
[tex]\[ 9x = 45 \][/tex]
To find the value of [tex]\( x \)[/tex], divide both sides of the equation by 9:
[tex]\[ x = \frac{45}{9} \][/tex]
[tex]\[ x = 5 \][/tex]
c. Find the length of each side:
Now that we know [tex]\( x = 5 \)[/tex], let's find the length of each side:
- The first three sides are each [tex]\( x \)[/tex], which means they are [tex]\( 5 \)[/tex] centimeters long.
- The last two sides are each [tex]\( 3x \)[/tex], so they are [tex]\( 3 \times 5 = 15 \)[/tex] centimeters long.
So, the side lengths of the pentagon are:
- Three sides measuring 5 centimeters each.
- Two sides measuring 15 centimeters each.
a. Write an equation for the perimeter:
The problem states that the pentagon's perimeter is the sum of its side lengths, which equals 45 centimeters. In this case, the sides are given as three sides of length [tex]\( x \)[/tex] and two sides of length [tex]\( 3x \)[/tex]. So, we can write the equation for the perimeter as:
[tex]\[ x + x + x + 3x + 3x = 45 \][/tex]
b. Solve the equation:
Let's simplify the equation:
[tex]\[ 3x + 6x = 45 \][/tex]
When simplified, this equation becomes:
[tex]\[ 9x = 45 \][/tex]
To find the value of [tex]\( x \)[/tex], divide both sides of the equation by 9:
[tex]\[ x = \frac{45}{9} \][/tex]
[tex]\[ x = 5 \][/tex]
c. Find the length of each side:
Now that we know [tex]\( x = 5 \)[/tex], let's find the length of each side:
- The first three sides are each [tex]\( x \)[/tex], which means they are [tex]\( 5 \)[/tex] centimeters long.
- The last two sides are each [tex]\( 3x \)[/tex], so they are [tex]\( 3 \times 5 = 15 \)[/tex] centimeters long.
So, the side lengths of the pentagon are:
- Three sides measuring 5 centimeters each.
- Two sides measuring 15 centimeters each.
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