Let’s solve each problem step by step. We’ll use the Pythagorean Theorem:
a² + b² = c², where
c is the hypotenuse (the longest side, opposite the right angle), and
a and
b are the legs.
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Problem 1:
Triangle with legs 3 and 4, find hypotenuse x.
Use:
x² = 3² + 4²
x² = 9 + 16
x² = 25
x = √25 =
5
Answer:
5 feet
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Problem 2:
Triangle with one leg 5.3, hypotenuse 10.1, find other leg x.
Use:
x² + 5.3² = 10.1²
x² + 28.09 = 102.01
x² = 102.01 - 28.09 = 73.92
x = √73.92 ≈
8.6 (rounded to nearest tenth)
Answer:
8.6 inches
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Problem 3:
Legs 5 and 9, find hypotenuse x in simplest radical form.
x² = 5² + 9² = 25 + 81 = 106
x = √106 → already simplified (106 has no perfect square factors besides 1)
Answer:
√106 yards
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Problem 4:
One leg 8 mi, hypotenuse 16 mi, find other leg x in simplest radical form.
x² + 8² = 16²
x² + 64 = 256
x² = 192
Simplify √192:
192 = 64 × 3 → √(64×3) = 8√3
Answer:
8√3 miles
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Problem 5:
Given a = 11 m, c = 15 m, find b in simplest radical form.
b² + 11² = 15²
b² + 121 = 225
b² = 104
Simplify √104:
104 = 4 × 26 → √(4×26) = 2√26
Answer:
2√26 meters
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Problem 6:
Given b = √5 yd, c = 4 yd, find a in simplest radical form.
a² + (√5)² = 4²
a² + 5 = 16
a² = 11
a = √11 → already simplified
Answer:
√11 yards
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Final Answer:
1. 5 ft
2. 8.6 in
3. √106 yd
4. 8√3 mi
5. 2√26 m
6. √11 yd
Parent Tip: Review the logic above to help your child master the concept of converse of the pythagorean theorem worksheet.
