45-45-90 Triangles

Front

What is a 45-45-90 triangle?

Back

A 45-45-90 triangle is an isosceles right triangle where the angles are 45 degrees, 45 degrees, and 90 degrees.

Front

What is the ratio of the sides in a 45-45-90 triangle?

Back

The ratio of the sides in a 45-45-90 triangle is 1:1:√2.

Front

If the legs of a 45-45-90 triangle are each 5, what is the length of the hypotenuse?

Back

The hypotenuse is 5√2.

Front

How do you find the length of the legs in a 45-45-90 triangle if the hypotenuse is known?

Back

Divide the length of the hypotenuse by √2.

Front

If the hypotenuse of a 45-45-90 triangle is 10√2, what are the lengths of the legs?

Back

Each leg is 10.

Front

What is the area of a 45-45-90 triangle with legs of length 4?

Back

The area is 8 square units.

Front

What is the perimeter of a 45-45-90 triangle with legs of length 6?

Back

The perimeter is 6 + 6 + 6√2 = 6(1 + √2).

Front

In a 45-45-90 triangle, if one leg is 3, what is the length of the other leg?

Back

The other leg is also 3.

Front

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

Back

The hypotenuse is √2 times the length of each leg.

Front

If the legs of a 45-45-90 triangle are x, what is the expression for the hypotenuse?

Back

The hypotenuse is x√2.