If the perimeter of an isosceles right triangle is 8(√2+1) cm, then the length of the hypotenuse of the triangle is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 8 cm
In an isosceles right-angle triangle, two perpendicular sides are equal.
Let the length of two perpendicular sides be 'a' and hypotenuse be 'a√2'.
a + a + a√2 = 8(√2+1)
2a + a√2= 8(√2+1).
a√2(√2 + 1) = 8(√2+1)
a = 4√2.
Hypotenuse = √2a
= √2 × 4√2 = 8.