Question

The area of an isosceles right angled triangle is $16c{m^2}$, then the length of the hypotenuse is
A. 8cm
B. 9cm
C. 10cm
D. 11cm

Answer 1

Hint: Here we will proceed by assuming one side of the triangle as x . Since the base and height of an isosceles right angled triangle will be the same so we equate the formula of area of triangle with the given area to find the base or height. Therefore using Pythagoras theorem we get the length of the hypotenuse.

Complete step-by-step answer:
Given area of the triangle = $\dfrac{1}{2} \times base \times height$
But base (B) = height (H)
$ \Rightarrow 16 = \dfrac{1}{2} \times B \times B$
$ \Rightarrow {B^2} = 32$
$ \Rightarrow B = 4\sqrt 2 cm$
Which is also equal to height (H)
Using Pythagoras theorem ,
$Hypotenuse{e^2} = bas{e^2} + heigh{t^2}$
$Hypotenuse = \sqrt {{{\left( {4\sqrt 2 } \right)}^2} + {{\left( {4\sqrt 2 } \right)}^2}} $
$Hypotenuse = \sqrt {32 + 32} = \sqrt {64} = 8cm$

Note: In such specific questions, we should remember to recall the concept of isosceles right angled triangles and equate the area to find the value of base(B) and then further use the Pythagoras theorem to get to the desired answer . Note that an isosceles triangle is a triangle with two sides of equal length .