Question : If the perimeter of an isosceles right triangle is $8(\sqrt{2}+1)$ cm, then the length of the hypotenuse of the triangle is:

Option 1: 8 cm

Option 2: 12 cm

Option 3: 10 cm

Option 4: 24 cm


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 15th Jan, 2024

Correct Answer: 8 cm


Solution : Given: The perimeter of an isosceles right triangle is $8(\sqrt{2}+1)$ cm.

The total of a triangle's sides is its perimeter.
Let the isosceles right triangle have equal sides of $x$ cm, then its hypotenuse is $\sqrt2x$ cm.
According to the question,
$x+x+\sqrt 2x=8(\sqrt{2}+1)$
⇒ $2x+\sqrt 2x=8(\sqrt{2}+1)$
⇒ $\sqrt2x(\sqrt 2+1)=8(\sqrt{2}+1)$
⇒ $x=\frac{8}{\sqrt2}$
⇒ $x=4\sqrt2$ cm
The length of the hypotenuse of the triangle = $\sqrt2\times 4\sqrt2=8$ cm.
Hence, the correct answer is 8 cm.

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