Question

Show that the triangle 𝐴𝐵𝐶 is a right-angled triangle; if: 𝐴𝐵 = 9 𝑐𝑚, 𝐵𝐶 = 40 𝑐𝑚 and 𝐴𝐶 = 41 𝑐𝑚.

Answer 1

Step: Checking if the sides of triangle satisfy the Pythagoras theorem

Given, 𝐴𝐵 = 9 𝑐𝑚, 𝐵𝐶 = 40 𝑐𝑚, 𝐴𝐶 = 41 𝑐𝑚

The given triangle will be right angled triangle, if it satisfies the Pythagoras theorem.


According to Pythagoras theorem,

$(Hypotenuse{)}^2$ = $(Perpendicular{)}^2$ + $(Base{)}^2$

$(41{)}^2$ = $(40{)}^2$ + $(9{)}^2$

[Hypotenuse = Longer side]

1681 = 1600 + 81

1681 = 1681

Thus, LHS = RHS

Hence, ∆ABC is a right-angled triangle.