Special Right Triangles (45-45-90)

Front

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The legs are of equal length, and the hypotenuse is √2 times the length of a leg.

Front

What is the relationship between the legs and hypotenuse in a 45-45-90 triangle?

Back

In a 45-45-90 triangle, if each leg has a length of 'a', then the hypotenuse has a length of 'a√2'.

Front

If the length of each leg of a 45-45-90 triangle is 6, what is the length of the hypotenuse?

Back

The hypotenuse is 6√2.

Front

What is the formula to find the hypotenuse in a 45-45-90 triangle?

Back

Hypotenuse = leg × √2.

Front

If the hypotenuse of a 45-45-90 triangle is 13√2, what is the length of each leg?

Back

Each leg is 13.

Front

What is the value of x in a 45-45-90 triangle if one leg is 7?

Back

x = 7√2 (hypotenuse).

Front

If the legs of a 45-45-90 triangle are both 9, what is the length of the hypotenuse?

Back

The hypotenuse is 9√2.

Front

What is the area of a 45-45-90 triangle with legs of length 5?

Back

Area = (1/2) × leg × leg = (1/2) × 5 × 5 = 12.5.

Front

How do you find the perimeter of a 45-45-90 triangle?

Back

Perimeter = leg + leg + hypotenuse = 2a + a√2.

Front

If one leg of a 45-45-90 triangle is 2, what is the length of the hypotenuse?

Back

The hypotenuse is 2√2.