MATH SOLVE

4 months ago

Q:
# The hypotenuse of a 45 -45 -90 triangle measures 128 cm what is the length of one leg of the triangle

Accepted Solution

A:

This is an isosceles triangle. The definition of an isosceles triangle is a triangle with at least two congruent sides and angles. If 2 angles on a triangle are congruent (in this case 45 and 45 are two congruent angles) then triangle is isosceles. Therefore the two sides of triangle will be congruent. We know that the triangle is a right triangle because it has a hypotenuse. If a triangle has a hypotenuse then it's a right triangle. We can apply the Pythagorean theorem: a^2 + b^2 = c^2

A and B are the legs and C is the hypotenuse.

We can plug C in the equation:

a^2 + b^2 = 128

What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?

8^2 + 8^2 = 128

64 + 64 = 128

128=128

Yes the value 8 works so the length of two legs of the triangle is 8.

A and B are the legs and C is the hypotenuse.

We can plug C in the equation:

a^2 + b^2 = 128

What do we know about the legs of the isosceles triangle? They are congruent so a and b have to be equal. From here it's simply guess and check. Will 8 work?

8^2 + 8^2 = 128

64 + 64 = 128

128=128

Yes the value 8 works so the length of two legs of the triangle is 8.