Question
A triangle is shown with a altitude of 7 cm, hypotenuse of 13 cm and base of 14 cm
Is this a right triangle? Why or Why not?
(1 point)
Responses
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse
Is this a right triangle? Why or Why not?
(1 point)
Responses
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
No, the Pythagorean Theorem does not hold true using 14 as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
Yes, the Pythagorean Theorem holds true using any of the sides as the hypotenuse
No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse
Answers
GPT-4o mini
To determine whether the triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b).
In this case, we have:
- The altitude (height) = 7 cm
- The hypotenuse = 13 cm (noting that the hypotenuse must be the longest side)
- The base = 14 cm (this should be treated as one of the legs)
To find out if it's a right triangle, we should examine if it satisfies the Pythagorean theorem:
1. Assume the leg opposite the altitude is one leg (let's call it leg a, which is 7 cm).
2. The other leg, which is the base, is 14 cm (let's call this leg b).
3. The hypotenuse is given as 13 cm (let's call this c).
The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
Substituting the values we have:
\[ 7^2 + 14^2 = 13^2 \]
Calculating each side:
- Left side:
\[ 7^2 + 14^2 = 49 + 196 = 245 \]
- Right side:
\[ 13^2 = 169 \]
Since 245 ≠ 169, the Pythagorean theorem does not hold true.
Thus, the correct response is:
**No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse.**
In this case, we have:
- The altitude (height) = 7 cm
- The hypotenuse = 13 cm (noting that the hypotenuse must be the longest side)
- The base = 14 cm (this should be treated as one of the legs)
To find out if it's a right triangle, we should examine if it satisfies the Pythagorean theorem:
1. Assume the leg opposite the altitude is one leg (let's call it leg a, which is 7 cm).
2. The other leg, which is the base, is 14 cm (let's call this leg b).
3. The hypotenuse is given as 13 cm (let's call this c).
The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]
Substituting the values we have:
\[ 7^2 + 14^2 = 13^2 \]
Calculating each side:
- Left side:
\[ 7^2 + 14^2 = 49 + 196 = 245 \]
- Right side:
\[ 13^2 = 169 \]
Since 245 ≠ 169, the Pythagorean theorem does not hold true.
Thus, the correct response is:
**No, the Pythagorean Theorem does not hold true using any of the sides as the hypotenuse.**