Question

Drag each triangle to the correct category.
For each set of side lengths, classify the triangle based on whether it is a right triangle.

1. 4,10,11

2. 4,4 square root of 32

3. 8,7, square root of 113

4. 4,4 square root of 24

5. 7,8,15


What is a right triangle and which is not a right triangle
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Answer 1

Answer:

$4,10,11$ not Right Triangle

$4, 4, \sqrt{32}$ Right Triangle

$8, 7, \sqrt{113}$ Right Triangle.

$4, 4, \sqrt{24}$ not Right Triangle.

$7, 8, 15$ not Right Triangle.

Step-by-step explanation:

To determine if a set of side lengths corresponds to a right triangle, the sides must satisfy the Pitagorean identity:

$side1^{2} + side2^{2} = hypotenuse^{2}$

Notice that the hypotenuse is always the greatest side of the set...

Let's plug the given values into the idenity above.

Option 1

$4^{2} + 10^{2} =_{?} 11^{2}$

$16 + 100 =_{?} 121$

$116 \neq 121$

Option 2

$4^{2} + 4^{2} =_{?} (\sqrt{32})^{2}$

$16 + 16 =_{?} 32$

$32 = 32$

Option 3

$8^{2} + 7^{2} =_{?} (\sqrt{113})^{2}$

$64 + 49 =_{?} 113$

$113 = 113$

Option 4

$4^{2} + 4^{2} =_{?} (\sqrt{24})^{2}$

$16 + 16 =_{?} 24$

$32 \neq 24$

Option 5

$7^{2} + 8^{2} =_{?} 15^{2}$

$49 + 64 =_{?} 225$

$113 \neq 121$

Answer 2

Answer:

see picture

Step-by-step explanation: