Question

The hypotenuse of an isosceles right triangle is 10cm long. Find the perimeter of the triangle

Answer 1

Isosceles triangle - this is triangle in wich two sides are equal to one another.

Perimeter of triangle - this is a sum of all sides.

Let a,b (are legs),c (is hypotenuse) be a sides of this triangle and a=b. So, perimeter of this triangle is equal to:
$P=a+b+c=2a+c$

This is an right angle triangle. So, we can use a Pythagorean Theorem.
$a^2+b^2=c^2\\a^2+a^2=c^2\\2a^2=c^2$

But c=10 cm. So:
$2a^2=10^2\\2a^2=100\\a^2=50\\a= \sqrt{50} =5 \sqrt{2}$

$b=a =5 \sqrt{2}$

Perimeter:
$P=2\cdot 5 \sqrt{2} +10=10 \sqrt{2} +10=10( \sqrt{2} +1)$ cm