Question

The perimeter of a certain polygon is 10.5 cm four sides of this pentagon have the same length as centimeters H and the other side has length of 1.7 cm as shown what is the value of HS.

Answer 1

The perimeter of any polygon is the sum of the length of the outline sides

From the attached picture we can see

A polygon with 5 sides

The lengths of 4 sides are h cm

The length of the 5th side is 1.7 cm

To find its perimeter add the length of the 5 sides

`h+h+h+h+1.7=P`

Since the perimeter is given 10.5 cm, then

P = 10.5

Substitute P by 10.5 in the equation above

`h+h+h+h+1.7=10.5`

Add the like terms on the left side

`\begin{gathered} (h+h+h+h)+1.7=10.5 \\ 4h+1.7=10.5 \end{gathered}`

Subtract 1.7 from both sides

`\begin{gathered} 4h+1.7-1.7=10.5-1.7 \\ 4h=8.8 \end{gathered}`

Divide both sides by 4

`\begin{gathered} (4h)/(4)=(8.8)/(4) \\ h=2.2 \end{gathered}`

The value of h is 2.2 cm

The answer is a

We can check the answer by adding the 5 sides, the answer must be 10.5

`\begin{gathered} 2.2+2.2+2.2+2.2+1.7= \\ 8.8+1.7= \\ 10.5\text{ cm} \end{gathered}`

The answer is correct