Sides of a triangle are given below. Determine whether it is a right triangle. In case of a right triangle,write the length of its hypotenuse.
$3 \text{ cm}, 8 \text{ cm}, 6 \text{ cm}$
$3 \text{ cm}, 8 \text{ cm}, 6 \text{ cm}$
(N/A) The given sides of the triangle are $3 \text{ cm}, 8 \text{ cm},$ and $6 \text{ cm}$.
According to the converse of the Pythagoras theorem,a triangle is a right triangle if the sum of the squares of the two smaller sides is equal to the square of the longest side.
Here,the squares of the sides are:
$3^2 = 9$
$6^2 = 36$
$8^2 = 64$
Checking the sum of the squares of the two smaller sides:
$3^2 + 6^2 = 9 + 36 = 45$
Since $45 \neq 64$ (i.e.,$3^2 + 6^2 \neq 8^2$),the condition for a right triangle is not satisfied.
Therefore,the given triangle is not a right triangle.
According to the converse of the Pythagoras theorem,a triangle is a right triangle if the sum of the squares of the two smaller sides is equal to the square of the longest side.
Here,the squares of the sides are:
$3^2 = 9$
$6^2 = 36$
$8^2 = 64$
Checking the sum of the squares of the two smaller sides:
$3^2 + 6^2 = 9 + 36 = 45$
Since $45 \neq 64$ (i.e.,$3^2 + 6^2 \neq 8^2$),the condition for a right triangle is not satisfied.
Therefore,the given triangle is not a right triangle.
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