Which of the following statements justifies why the triangle shown below is not a right triangle?

Mathematics

2 answers:

Musya8 [376]2 years ago

7 0

Answer:

the sum of the of the square of the opposite and adjacent does not equal the hypotenuse

mestny [16]2 years ago

5 0

Answer:

Step-by-step explanation:

For the triangle to be right then the square on the hypotenuse must equal the sum of the squares on the other 2 sides

13² = 169

12² + 4² = 144 + 16 = 160

Since 4² + 12² ≠ 13² then triangle is not right angled

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Sunny_sXe [5.5K]

How about this (see attached image):

Use the four cuts as shown in the image (red lines).

Then assemble 5 equal squares by the numbers: 1 center square and the rest are pieced together using two pieces as shown. All five together add up to the same area as original square because we use all pieces.

The way one gets a hint toward a solution is to see how an area of a square of length 1 can be split into 5 equal square areas:

$1^2 = 5\cdot x^2\\x = \frac{\sqrt{5}}{5} = \sqrt{\frac{2^2}{5^2}+\frac{1^2}{5^2}}$

which indicates we need to find a a triangle with sides 2 and 1 to get the hypotenuse of the right length. That gave rise to the cut pattern (if you look carefully, there are triangles with those side lengths).