Question

I need some help to classify this triangle pls

Answer 1

Answer:

We conclude that $\sqrt{5}, \sqrt{5},\sqrt{10}$ is an isosceles right triangle.

Step-by-step explanation:

Given the sides of a triangle

$\sqrt{5}, \sqrt{5},\sqrt{10}$

Given that the two sides are equal. Thus, it must be an isosceles triangle.

Let us check whether it is an isosceles right triangle or not.

We know that for a right-angled triangle with sides a, b and the hypotenuse c is defined as:

$c=\sqrt{a^2+b^2}$

Given

$a=\sqrt{5}$

$b=\sqrt{5}$

now substituting $a=\sqrt{5}$ and $b=\sqrt{5}$ in the equation

$c=\sqrt{a^2+b^2}$

$c=\sqrt{\left(\sqrt{5}\right)^2+\left(\sqrt{5}\right)^2}$

$c=\sqrt{10}$

Thus,

$a=\sqrt{5}$

$b=\sqrt{5}$

$c=\sqrt{10}$

Which satisfies the given side lengths $\sqrt{5}, \sqrt{5},\sqrt{10}$

Therefore, we conclude that $\sqrt{5}, \sqrt{5},\sqrt{10}$ is an isosceles right triangle.