Question

Which of triangle whose sides are given below are right angled?

(a) AB = 89, AC = 80, BC = 39

(b) AB = 57, AC = 50, BC = 45

(c) AC = 34, AB = 20, BC = 21

(d) AC = 50, AB = 32, BC = 20

The question was asked in an interview.

I want to ask this question from Pythagoras Theorem topic in chapter Triangles of Mathematics – Class 10

Answer 1

Correct choice is (a) AB = 89, AC = 80, BC = 39

The best I can explain: In (a), applying Pythagoras Theorem,

AC^2 + BC^2 = 80^2 + 39^2 = 7921 = AB^2

Hence, this is a right angled triangle.

Now, in (b) applying Pythagoras Theorem,

AC^2 + BC^2 = 50^2 + 45^2 = 4525 ≠ AB^2

Hence, this is not a right angled triangle.

Now, in (c) applying Pythagoras Theorem,

AB^2 + BC^2 = 20^2 + 21^2 = 841 ≠ AC^2

Hence, this is not a right angled triangle.

Now, in (d) applying Pythagoras Theorem,

AB^2 + BC^2 = 32^2 + 20^2 = 1424 ≠ AC^2

Hence, this is not right angled triangle.