Try to find an example of two right triangles that have the same hypotenuse but have different side lengths.
False
Practice makes perfect
We are asked to determine whether any two right triangles with the same hypotenuse have the same area. To do this, let's find an example of two right triangles that have the same hypotenuse but have different side lengths.
7, 24 &and 25
15, 20 &and 25
These are two of the Common Pythagorean Triples. Now, we will find the area of each of the triangles and see if they are equal. Let's recall that in right triangles each of the legs is a height of the triangle while the other leg is a base.
1/2&( 7)(24)=84
1/2&(15)(20)=150
As we can see, the areas are not equal. Since we found an example that does not satisfy the given statement, the correct answer is false.
