The area of an isosceles right angled triangle is 121 cm2 . Find its hypotenuse
Answer & explanation
Correct answer: option 3
Area of triangle = \(\frac{1}{2}\)× base × height
According to Pythagoreans theorem
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
Let the base and height of the isosceles triangle be ‘x’
Area of triangle = \(\frac{1}{2}\)× base × height
= 121 = \(\frac{1}{2}\)× x × x
= x2 = 242
= x = √242 = 11√2
We know that,
(AC)2 = (AB)2 + (BC)2
= (AC)2 = (11√2)2 + (11√2)2
= (AC)2 = 242 + 242
= (AC)2 = 484
= AC = √484 = 22 cm