This worksheet asks you to find the length of the side marked
x in each right triangle. Since all triangles are right-angled (marked with a square), we can use the
Pythagorean Theorem:
>
a² + b² = c²
Where:
-
a and
b are the legs (the two sides that form the right angle),
-
c is the hypotenuse (the side opposite the right angle — always the longest side).
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Let’s solve each one step by step.
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Problem 1:
Legs: 15 cm and 8 cm
Hypotenuse: x
Use Pythagorean Theorem:
x² = 15² + 8²
x² = 225 + 64
x² = 289
x = √289
x = 17 cm
✔ Answer: x = 17 cm
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Problem 2:
One leg: 9 cm
Hypotenuse: 20 cm
Other leg: x
Here, x is a leg, so rearrange the formula:
x² + 9² = 20²
x² + 81 = 400
x² = 400 - 81
x² = 319
x = √319 ≈ 17.86 cm
But since this is likely expecting an exact value or simplified radical, let's check if 319 is a perfect square → it’s not (17²=289, 18²=324). So unless specified, we leave as √319 or approximate.
However, looking at other problems, they may expect decimal approximations or exact values. Let’s compute decimal:
√319 ≈
17.86 cm
But wait — let me double-check the diagram. If 20 is hypotenuse, and 9 is leg, then yes, x = √(400 - 81) = √319.
But perhaps there’s a typo? 9-12-15 or 9-40-41? No. 319 is correct.
✔ Answer: x = √319 cm ≈ 17.86 cm
*(If your teacher expects decimal, round to 1 decimal place: 17.9 cm)*
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Problem 3:
Legs: 6.5 cm and 10.2 cm
Hypotenuse: x
x² = 6.5² + 10.2²
x² = 42.25 + 104.04
x² = 146.29
x = √146.29 ≈
12.095 cm
Rounded to 1 decimal place:
12.1 cm
✔ Answer: x ≈ 12.1 cm
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Problem 4:
One leg: 8.4 cm
Hypotenuse: 10.5 cm
Other leg: x
x² + 8.4² = 10.5²
x² + 70.56 = 110.25
x² = 110.25 - 70.56
x² = 39.69
x = √39.69 =
6.3 cm (since 6.3 × 6.3 = 39.69)
✔ Answer: x = 6.3 cm
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Problem 5:
One leg: 5 cm
Hypotenuse: 13 cm
Other leg: x
x² + 5² = 13²
x² + 25 = 169
x² = 144
x = √144 =
12 cm
✔ Answer: x = 12 cm
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✔ Final Answers:
1.
x = 17 cm
2.
x = √319 cm ≈ 17.9 cm *(or exact form if preferred)*
3.
x ≈ 12.1 cm
4.
x = 6.3 cm
5.
x = 12 cm
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📌 *Note: For problem 2, if you’re expected to give an exact answer, write √319. If decimal, round to 1 decimal place: 17.9 cm.*
Parent Tip: Review the logic above to help your child master the concept of solving pythagorean theorem worksheet.
