The perimeter of a certain isosceles right triangle is 10

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The perimeter of a certain isosceles right triangle is 10 + 10√2 cm. What is the length of the hypotenuse of the triangle ?

1. 5 cm
2. 10 cm
3. 52cm
4. 10√2cm

Correct Option: B

AB = BC = x cm.
∴ AC = √AB² + BC²
= √x² + x² = √2x² = 2x cm.
∴ AB + BC + CA = 10 + 10√2
⇒ 2x + √2x = 10 + 10√2
⇒ √2x (√2 + 1) = 10(1 + √2)
⇒ √2x = 10 cm. = AC