Question

# Find the unknown length and round the answer to the nearest tenth.

Hint:

### Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.

If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as

c2= a2 + b2

## The correct answer is: Hence, the length of the missing side is 23.68 cm.

### Using pythagoras theorem:

c^{2}= a^{2} + b^{2}

c = Length of Hypotenuse

a = Length of perpendicular

b = Length of base

a)

c = 5.2 m and a = 2.4 m

So,

c^{2}= a^{2} + b^{2}

5.2^{2} = 2.4^{2} + b^{2}

b^{2} = 5.2^{2} - 2.4^{2}

b^{2} = 24.64

b = 4.96 m

Final Answer:

Hence, the length of the missing side is 4.96 m.

b)

c = 10 cm and b = 3 cm

So,

c^{2}= a^{2} + b^{2}

10^{2} = a^{2} + 3^{2}

a^{2} = 10^{2} - 3^{2}

a^{2} = 91

a = 9.54 cm

Final Answer:

Hence, the length of the missing side is 9.54 cm.

c)

a = 7 m and b = 5 m

So,

c^{2}= a^{2} + b^{2}

c^{2} = 7^{2} + 5^{2}

c^{2} =74

c = 8.6 m

Final Answer:

Hence, the length of the missing side is 8.6 m.

d)

c = 25 cm and b = 8 cm

So,

c^{2}= a^{2} + b^{2}

25^{2} = a^{2} + 8^{2}

a^{2} = 25^{2} - 8^{2}

a^{2} = 561

a = 23.68 cm

Hence, the length of the missing side is 23.68 cm.

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