# The sides of a pentagon are represented by x , x+4, 2x+1, 2x+2, 3x. Determine each side if the perimeter is 52.

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The perimeter of the pentagon can be calculated as sum of the measure of the sides. Thus adding the given values of the sides of pentagon :

Perimeter = (x) + (x + 4) + (2x + 1) + (2x + 2) + (3x)

= 7x + 7

Value of perimeter is given as 52. Therefor:

9x + 7 = 52

==> 9x = 52 - 7 = 45

x = 45/9 = 5

Substituting this value of x in the given measures of the side we get the measure of each side:

x = 5,

x + 4) = 5 + 4 = 9

2x + 1 = 2*5 + 1 = 11

2x + 2 = 2*5 + 2 = 12

3x = 3*5 = 15

Answer:

Sides of pentagon are:

5, 9, 11, 12 and 15

The perimeter p is the sum of all the sides of the pentagon.

So, P = x+(x+4)+(2x+1)+(2x+2) +3x

P = 9x+7. But this is give to be 52.

Therefore , 9x+7 = 52.

9x = 52-7 = 45

x = 45/9 = 5.

Therefore sides of the pentagon are:

x = 5

x+4 = 5+4 = 9

2x+1 = 2*5+1 = 11

2x+2 = 2*5+2 = 12

3x = 3*5 = 15.

Tally: Sumof the sides = p = 5+9+11+12+15 = 52.

Since the pentagon is not regular, the lengths of the sides are not equal.

The perimeter of any geometric shape is the sum of the lengths of the sides of that shape.

We'll note the perimeter as P and the sides as s1, s2...

Since the pentagon has 5 sides, we'll calculate the perimeter as:

P = s1 + s2 + s3 + s4 + s5

We know, from enunciation, the value of the perimeter and an expression for each side. We'll substitute all we know in the formula of perimeter.

52 = x + (x+4) + (2x+1) + (2x+2) + 3x

We'll remove the brackets from the right side:

52 = x + x + 4 + 2x + 1 + 2x + 2 + 3x

We'll combine like terms:

52 = 9x + 7

We'll subtract 52 both sides:

0 = 9x + 7 - 52

0 = 9x - 45

We'll add 45 both sides and we'll use symmetric property:

9x = 45

We'll divide by 9:

x = 5

Now, we'll determine each side:

s1 = x

**s1 = 5**

s2 = x+4

s2 = 5+4

**s2 = 9**

s3 = 2x + 1

s3 = 2*5 + 1

**s3 = 11**

s4 = 2x + 2

**s4 = 12**

s5 = 3x

**s5 = 15**