Question

How do i solve this ?

Answer 1

`2√(2)`

Explanation:

The given triangle is an isosceles triangle. However, one can see that it has a right angle (indicated by the box around the angle). Thus the triangle is a (45 - 45 - 90) triangle. A (45- 45 - 90) triangle is the only right isosceles triangle. One of the properties of a right isosceles triangle is that its sides follow the following ratio,

`a;a;a√(2)`

Where (a) represents the legs of the right triangle, the sides that are adjacent to the right angle, in this case, the congruent sides. (
`a√(2)`) is the hypotenuse, the side opposite the right angle.

It is given that the hypotenuse is equal to (4), one is asked to find the length of the legs. To do so, divide the hypotenuse by (
`√(2)`) to find the legs. One can do this because the triangle is a (45 - 45 - 90) triangle, thus it must follow the ratio of the sides.

`=(4)/(√(2))`

Rationalize the denominator,

`(4)/(√(2))\\\\=(4√(2))/(2)\\\\=2√(2)`