This is a math worksheet asking to find the missing side of each right triangle. To solve this, I will use the Pythagorean theorem, which states that for any right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (the legs). The formula is $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.
I will solve each problem one by one.
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Problem 1
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Given: Two legs are 12 in and 5 in.
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Find: The hypotenuse.
-
Calculation:
$$
c^2 = 12^2 + 5^2 = 144 + 25 = 169
$$
$$
c = \sqrt{169} = 13
$$
-
Answer: 13 in
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Problem 2
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Given: Two legs are 9 cm and 12 cm.
-
Find: The hypotenuse.
-
Calculation:
$$
c^2 = 9^2 + 12^2 = 81 + 144 = 225
$$
$$
c = \sqrt{225} = 15
$$
-
Answer: 15 cm
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Problem 3
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Given: One leg is 24 m, and the hypotenuse is 25 m.
-
Find: The other leg.
-
Calculation:
$$
a^2 + 24^2 = 25^2
$$
$$
a^2 + 576 = 625
$$
$$
a^2 = 625 - 576 = 49
$$
$$
a = \sqrt{49} = 7
$$
-
Answer: 7 m
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Problem 4
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Given: One leg is 16 in, and the hypotenuse is 20 in.
-
Find: The other leg.
-
Calculation:
$$
a^2 + 16^2 = 20^2
$$
$$
a^2 + 256 = 400
$$
$$
a^2 = 400 - 256 = 144
$$
$$
a = \sqrt{144} = 12
$$
-
Answer: 12 in
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Problem 5
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Given: Two legs are 6 cm and 8 cm.
-
Find: The hypotenuse.
-
Calculation:
$$
c^2 = 6^2 + 8^2 = 36 + 64 = 100
$$
$$
c = \sqrt{100} = 10
$$
-
Answer: 10 cm
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Final Answers:
1. 13 in
2. 15 cm
3. 7 m
4. 12 in
5. 10 cm
Parent Tip: Review the logic above to help your child master the concept of right triangle pythagorean theorem worksheet.
