Question

Help with the question below would be much appreciated :)

Answer 1

B

Explanation:

In an isosceles triangle, the altitude is the median so the altitude splits the base into two segments with lengths of 5. We notice that x is part of a right triangle with legs of 5 and 12, therefore, using the 5 - 12 - 13 Pythagorean Triple, x = 13.

Answer 2

(B) 13

Explanation:

This isosceles triangle is broken up into two parts, both are right triangles.

To find the length of a missing side in a right triangle, we use the Pythagorean Theorem -
`a^2+b^2=c^2`. where one of the legs is a, the other leg is b, and the hypotenuse is c.

We know that one of the legs is 12, and since the base of the triangle is 10, the leg of one of the right triangles is 5.

Let's solve.

`5^2+12^2=c^2\\25+144=c^2\\169=c^2\\\\√(169) =c\\13=c`

So, c is 13, therefore the hypotenuse is 13, therefore x is 13.

Hope this helped!