Question

A DEF is a right triangle.

Answer 1

Answer:

The statement is false because ΔDEF is not a right triangle.

Step-by-step explanation:

We can figure out if this triangle is a right triangle by using the Pythagorean Theorem. The Pythagorean Theorem is a² + b² = c².

a = 26

b = 27

c = 48

Now, let's plug these numbers into the formula.

(26)² + (27)² = (48)²

676 + 729 = 2304

1405 = 2304

1405 does not equal to 2304.

So, ΔDEF is not a right triangle.

Answer 2

The Pythagorean Theorem states that in a right triangle, $a^{2} + b^{2} = c^{2}$, where a and b are the legs and c is the hypotenuse.

Plugging in this formula, we can identify if DEF is a right triangle.

$25^{2} +27^{2} = c^{2}$

The first step is to plug in our known values.

$625 + 729 = c^{2}$

Next, we'll square both values available.

$1354 = c^{2}$

From there, we'll add the values together.

$36.7967.. = c$

Finally, we'll find the square root of our value to get c.

Since our answer is ~36, and the value we're given for the hypotenuse is 48, this is not a right triangle since the values aren't the same.

Therefore, the answer is False.

Hope this helped! :)