If the perimeter of a right-angled isosceles triangle is (4\sqrt2 + 4) cm, the length of the hypotenuse is:

Area and Perimeter Practice Test 3

Question : 11 of 40

Marks: +1, -0

If the perimeter of a right-angled isosceles triangle is

(4√2 + 4)

cm, the length of the hypotenuse is:

Solution:

Let equal sides of isosceles right triangle be x cm;
then hypotenuse will be

√2

x cm.
Since, x + x +

√2x

4√2 +4

⇒

(2+√2)x

4(√2+1)

∴ x =

{4(√2+1)}/{√2(√2+1)}

2√2

nce, length of hypotenuse =

2√2 ×√2

= 4 cm

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