Question

An eighth-grade student said the side length 41,40 and 9 do not form a right triangle, because

9^2+41^2=1762 and 40^2=1600 and 1762 does not equal 1600. What error did the student makes

Answer 1

Error was CHOOSING the CORRECT hypotenuse in the given sides.

H = 41 units

Explanation:

Here, the given sides of the triangle are: 41,40 and 9

Now, as we know in a RIGHT ANGLED TRIANGLE:

The longest side is the HYPOTENUSE.

So, here H = 41

Now, by PYTHAGORAS THEOREM:

`({PERPENDICULAR)^2 + ( BASE)^2 = (HYPOTENUSE)^`

`(40)^2 + (9)^2  = 1600 + 81  = 1681 = (41)^2\\\implies (40)^2 + (9)^2  = (41)^2`

Hence, Pythagoras theorem for Right angled triangle is SATISFIED

So, error was CHOOSING the CORRECT hypotenuse in the given sides.

The correct H = 41 units and NOT 40 units.