Calculate the Second Base Length: Trapezoid with 300% Perimeter Ratio

Perimeter Ratios with Unknown Trapezoid Side

Calculate the length of the second base given that the perimeter of the trapezoid in the drawing is 300% of the length of the base.

888171717121212

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:08 Let's start by finding side A B.
00:11 First, convert the percentage into a fraction. This will make calculations easier.
00:20 Now, simplify the fraction as much as possible.
00:25 The perimeter of a trapezoid is the sum of all its sides.
00:38 So, let's plug in the given values to find side A B.
00:59 Next, we'll isolate A B on one side of the equation.
01:12 And there you have it! We've solved the problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Calculate the length of the second base given that the perimeter of the trapezoid in the drawing is 300% of the length of the base.

888171717121212

2

Step-by-step solution

To solve this problem, we'll follow these steps:

  • Step 1: Calculate the total perimeter as 300% of the known base 1717.
  • Step 2: Use the perimeter formula to isolate the unknown base.
  • Step 3: Solve for the unknown base.

Now, let's work through each step:
Step 1: Given that the base 1717 is part of the perimeter calculation and that the perimeter is 300% of this base, we have: P=3×17=51 P = 3 \times 17 = 51

Step 2: Using the perimeter formula for a trapezoid P=a+b+c+dP = a + b + c + d, where a=17a = 17, c=8c = 8, d=12d = 12, and bb is the unknown base, we have: 51=17+8+12+b 51 = 17 + 8 + 12 + b

Step 3: Solve for the unknown base bb: 51=37+b 51 = 37 + b b=5137 b = 51 - 37 b=14 b = 14

Therefore, the length of the second base of the trapezoid is 14 14 .

3

Final Answer

14

Key Points to Remember

Essential concepts to master this topic
  • Formula: Perimeter equals sum of all four trapezoid sides
  • Technique: Calculate 300%×17=3×17=51 300\% \times 17 = 3 \times 17 = 51
  • Check: Verify 17+14+8+12=51 17 + 14 + 8 + 12 = 51 equals our perimeter ✓

Common Mistakes

Avoid these frequent errors
  • Calculating percentage incorrectly as addition instead of multiplication
    Don't add 300 to the base length = 317! This treats percentage as addition, not multiplication. The perimeter becomes impossibly large. Always multiply: 300% = 3.00, so 300% of 17 = 3 × 17 = 51.

Practice Quiz

Test your knowledge with interactive questions

Given the trapezoid:

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What is the area?

FAQ

Everything you need to know about this question

What does 300% of the base length mean?

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300% means 3 times the original amount. So if the base is 17, then 300% of 17 = 3×17=51 3 \times 17 = 51 . This becomes our total perimeter.

Why do we add all four sides for the perimeter?

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The perimeter is the distance around the entire shape. For any quadrilateral (including trapezoids), you must add all four sides: base₁ + base₂ + side₁ + side₂.

How do I know which side is the unknown base?

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Look at the diagram carefully! The trapezoid has two parallel sides (bases). One base is labeled 17, and we need to find the other base. The sides labeled 8 and 12 are the non-parallel sides.

Can I solve this without knowing what 300% means?

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No! Understanding percentages is crucial here. 300% = 300/100 = 3.0. When we say "300% of something," we multiply that something by 3. Practice: 200% of 10 = 2 × 10 = 20.

What if my answer doesn't make sense geometrically?

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Always check if your trapezoid can actually exist! The answer should be positive and reasonable compared to other sides. If you get a negative number or something impossibly large, recheck your calculations.

Is there a shortcut to solve this faster?

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Yes! Once you know the perimeter is 51, immediately subtract the known sides: 5117812=14 51 - 17 - 8 - 12 = 14 . This gives you the unknown base directly.

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