Question

Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse? 6 cm cm 12 cm cm

Answer 1

Answer

16.97 cm

Explanation

A triangle having the angles 45°-45°-90° shows that it is an isosceles triangle.

The 2 legs are equal.

Using the Pythagoras theorem;

c² = a² + b²

Where a and b are the lengths of the legs and c is the hypotenuse.

c² = a² + b²

c² = 12² + 12²

    = 144 + 144

    = 288

c = √288

  = 16.97 cm

There is no correct answer in your choices. The length of the hypotenuse is 16.97 cm.

 

Answer 2

The Pythagorean theorem can only be applied to right triangles. The right triangle may have an isosceles triangle also if two smaller sides are of the same length. If a right triangle is isosceles then the triangle is called the right-isosceles triangle. The length of hypotenuse is 16.97 cm.

The side opposite to the equal angle of a triangle are equal therefore the angles 45°-45°-90° is an isosceles triangle.

Apply the Pythagoras theorem and solve it further.

$c^2=a^2+b^2$

Where a and b are the lengths of the legs and c is the hypotenuse.

Thus,

$\begin{aligned}c^2&=12^2+12^2\\c^2&=144+144\\c^2&=288\\c=&\sqrt{288}\\c&=16.97 \end{aligned}$

The length of the hypotenuse is 16.97 cm.

To know more about an isosceles triangle, please refer to the link:

https://brainly.com/question/7830547