**Using pythagorean theorem worksheet :**

Worksheet given in this section is much useful to the students who would like to practice problems on "Pythagorean theorem".

In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.

If a and b are legs and c is the hypotenuse, then

a² + b² = c²

1. In the right triangle given below, find the length of the missing side using Pythagorean theorem.

2. In the right triangle given below, find the length of the missing side using Pythagorean theorem.

3. In the right triangle given below, find the length of the missing side using Pythagorean theorem.

4. In the right triangle given below, find the length of the missing side using Pythagorean theorem.

**Problem 1 : **

In the right triangle given below, find the length of the missing side using Pythagorean theorem.

**Solution :**

**Step 1 : **

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b² = c²

**Step 2 :**

Substitute the given measures.

7² + 24² = c²

**Step 3 :**

Solve the equation for c.

7² + 24² = c²

Simplify.

49 + 576 = c²

625 = c²

Write 625 as a perfect square (625 = 25²).

25² = c²

Get rid of the square on both sides.

25 = c

Hence, the length of the hypotenuse is 25 inches.

**Problem 2 : **

In the right triangle given below, find the length of the missing side using Pythagorean theorem.

**Solution :**

**Step 1 :**

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b² = c²

**Step 2 :**

Substitute the given measures.

a² + 12² = 15²

**Step 3 :**

Solve the equation for c.

Simplify.

a² + 144 = 225

Subtract 144 from both sides.

a² + 144 - 144 = 225 - 144

a² = 81

Write 81 as a perfect square (81 = 9²).

a² = 9²

Get rid of the square on both sides.

a = 9

Hence, the length of the leg is 9 centimeters.

**Problem 3 : **

In the right triangle given below, find the length of the missing side using Pythagorean theorem.

**Solution :**

**Step 1 :**

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b² = c²

**Step 2 :**

Substitute the given measures.

30² + 40² = c²

**Step 3 :**

Solve the equation for c.

30² + 40² = c²

Simplify.

900 + 1600 = c²

2500 = c²

Write 2500 as a perfect square (2500 = 50²).

50² = c²

Get rid of the square on both sides.

50 = c

Hence, the length of the hypotenuse is 50 ft.

**Problem 4 : **

In the right triangle given below, find the length of the missing side using Pythagorean theorem.

**Solution :**

**Step 1 :**

If a and b are legs and c is the hypotenuse, write Pythagorean for the above right triangle

a² + b² = c²

**Step 2 :**

Substitute the given measures.

a² + 40² = 41²

**Step 3 :**

Solve the equation for c.

Simplify.

a² + 1600 = 1681

Subtract 1600 from both sides.

a² + 1600 - 1600 = 1681 - 1600

a² = 81

Write 81 as a perfect square (81 = 9²).

a² = 9²

Get rid of the square on both sides.

a = 9

Hence, the length of the leg is 9 inches.

After having gone through the stuff given above, we hope that the students would have understood "Using pythagorean theorem worksheet".

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