The sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side. True or False?

Isosceles triangles are triangles that have two equal sides. Isosceles triangles have many interesting properties and applications. Let's check out one of them in this section.

Answer: It is false that the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.

Let's understand the solution in detail.

Explanation:

The statement given is incorrect. Let's verify it with the help of an example.

Let ABC be an isosceles triangle as shown, with AB = AC = 4 and BC = 5.

Now, let's check the formula.

According to the statement, the formula should be √AB + √AC = √BC.

√AB = √4, √AC = √4, √BC = √5

But the equation √AB + √AC = √BC is not true as √4 + √4 is equal to 4 which is not equal to √5.

Hence, it is false that the sum of the square roots of any two sides of an isosceles triangle is equal to the square root of the remaining side.