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

Q: Why do we write 2(8) + 3x instead of just adding all sides?

Writing 2(8) + 3x groups the known and unknown sides clearly! This shows we have two sides of 8 cm each plus three sides of x cm each, making the equation easier to solve.

Q: How do I know which sides are equal to each other?

Read the problem carefully! It says 'two sides are equal and 8 cm each' and 'the other three sides are equal to each other'. This tells us exactly which sides share the same length.

Q: Can a pentagon have sides with different lengths?

Yes! A regular pentagon has all equal sides, but an irregular pentagon can have different side lengths. This problem describes an irregular pentagon with two groups of equal sides.

Q: How do I check if my perimeter calculation is correct?

Add up all five sides using your answer: $ 8 + 8 + 5 + 5 + 5 = 31 $ cm. If this equals the given perimeter, your solution is correct!

Perimeter Problems with Mixed Side Lengths

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

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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

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.

Final Answer

$x=5$

Key Points to Remember

Essential concepts to master this topic

Setup: Define unknown variable and write perimeter equation systematically
Technique: Group known sides: 2(8) + 3x = 31 becomes 16 + 3x = 31
Check: Verify total perimeter: 8 + 8 + 5 + 5 + 5 = 31 cm ✓

Common Mistakes

Avoid these frequent errors

Adding all sides without defining variables first
Don't just write 8 + 8 + x + x + x = 31 without clearly defining what x represents! This leads to confusion about which sides are equal. Always define your variable first: 'Let x = length of each unknown side', then write 2(8) + 3x = 31.

Practice Quiz

Test your knowledge with interactive questions

Solve for X:

$$ 3x=18 $$

FAQ

Everything you need to know about this question

Why do we write 2(8) + 3x instead of just adding all sides?

Writing 2(8) + 3x groups the known and unknown sides clearly! This shows we have two sides of 8 cm each plus three sides of x cm each, making the equation easier to solve.

How do I know which sides are equal to each other?

Read the problem carefully! It says 'two sides are equal and 8 cm each' and 'the other three sides are equal to each other'. This tells us exactly which sides share the same length.

What if I get a negative answer for the side length?

A negative side length doesn't make sense! Check your arithmetic - you might have subtracted incorrectly. In this problem, $31 - 16 = 15$ , so $x = 5$ (positive).

Can a pentagon have sides with different lengths?

Yes! A regular pentagon has all equal sides, but an irregular pentagon can have different side lengths. This problem describes an irregular pentagon with two groups of equal sides.

How do I check if my perimeter calculation is correct?

Add up all five sides using your answer: $8 + 8 + 5 + 5 + 5 = 31$ cm. If this equals the given perimeter, your solution is correct!

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