Solve for Unknown Side Length: Pentagon with Two 8cm Sides and Equal Remaining Sides

A pentagonal figure, two of its sides are equal and the length of each is 8 cm, the other three sides are equal to each other.

The perimeter of the pentagon is equal to 31 cm, write an equation based on the data and determine the unknown

Video Solution

Solution Steps

00:16 Let's find X. Our first step is to identify what we're looking for.

00:21 Now, draw a pentagon. This will help us visualize the problem.

00:29 We know that two sides are each 8 units long. This is given data.

00:34 The other sides are equal, and we'll call them X. Let's mark these unknown sides with X.

00:49 The perimeter of the pentagon is the total of all its side lengths.

01:06 Let's gather like terms together to simplify our equation.

01:13 Rearrange the equation so that X is on one side.

01:25 Now, let's isolate X to find its value.

01:30 And there you have it! This is how we solve the problem.

Step-by-Step Solution

Let's solve the problem step-by-step:

Step 1: Understand that the problem gives us a pentagon with a total perimeter of 31 cm. The sides are structured so that two of them are each 8 cm, and the remaining three sides are equal in length.
Step 2: Let's define the length of each of the three equal sides as $x$ cm. Therefore, we can express the perimeter of the pentagon as: $2 \times 8 + 3x = 31$ .
Step 3: First, calculate the total length contributed by the two known sides: $2 \times 8 = 16$ cm.
Step 4: Substitute this into the perimeter equation: $16 + 3x = 31$ .
Step 5: Solve for $x$ by isolating the unknown variable:
Subtract 16 from both sides: $3x = 31 - 16$ .
Simplify the right-hand side: $3x = 15$ .
Divide both sides by 3: $x = \frac{15}{3} = 5$ .

Therefore, each of the three unknown sides has a length of $x = 5$ cm.