State whether the following statement is true or false:

A right triangle is possible with the sides of length 8 cm, 6 cm and 10 cm.

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True

False

answer is A.

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Detailed Solution

It is given that a right triangle is possible with the sides of length 8 cm, 6 cm and 10 cm.
We know that Pythagoras theorem states that

H^{2} = B^{2} + P^{2}

We take the longest side to be the hypotenuse and the other two will be the base and perpendicular.
H = 10 cm, P = 6 cm and B = 8 cm.
LHS =

H^{2} = 1 0^{2}

= 100

RHS =

B^{2} + P^{2} = 8^{2} + 6^{2}

= 64 + 36

= 100

Since LHS = RHS, the condition for Pythagoras theorem is satisfied.
So, a right triangle with given dimensions is possible.
Hence the given statement is true.
Therefore, the correct option is 1.

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