Question

If the altitude of an isosceles right triangle has a length of x units, what is the length of one leg of the large right triangle in terms of x?

x units
x units
x units
2x units

Answer 1

x units

Explanation:

SInce it is a right triangle, one of its angles measures 90 °.

And it is also an isoceles triangle, so the other two angles must measure the same, I will call this measure a.

The sum of the internal angles of a triangle is 180 °, so:

90° + 2a = 180

2a = 90°

a = 45°

One of the sides of the right angle measures x because it is the height, and this measure is opposite to an angle of 45°.

And because the other side of the right angle is also opposite to an angle of 45°, it must also measure x.

See the attached image:

Answer 2

(√2)x units

Explanation:

x is one leg of another isosceles right triangle whose hypotenuse is the leg of interest. The hypotenuse of an isosceles right triangle is √2 times the leg length, so the leg of the large triangle is ...

(√2)x . . . . units