select 3 side lengths that can form a right triangle. 11 feet 13 feet 15 feet 84 feet 85 feet 99 feet

Question

Accepted Answer

# Explanation:
## Step1: Recall the Pythagorean theorem
For a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side).
## Step2: Check each combination
- For $11$, $13$, $15$:
$11^{2}+13^{2}=121 + 169=290$, and $15^{2}=225$. Since $290
eq225$, these do not form a right - triangle.
- For $11$, $84$, $85$:
$11^{2}+84^{2}=121+7056 = 7177$, and $85^{2}=7225$. Since $7177
eq7225$, these do not form a right - triangle.
- For $13$, $84$, $85$:
$13^{2}+84^{2}=169 + 7056=7225$, and $85^{2}=7225$. Since $13^{2}+84^{2}=85^{2}$, these form a right - triangle.
- For $15$, $84$, $85$:
$15^{2}+84^{2}=225+7056 = 7281$, and $85^{2}=7225$. Since $7281
eq7225$, these do not form a right - triangle.
- For $11$, $15$, $99$:
$11^{2}+15^{2}=121+225 = 346$, and $99^{2}=9801$. Since $346
eq9801$, these do not form a right - triangle.
- For $13$, $15$, $99$:
$13^{2}+15^{2}=169+225 = 394$, and $99^{2}=9801$. Since $394
eq9801$, these do not form a right - triangle.
- For $15$, $84$, $99$:
$15^{2}+84^{2}=225 + 7056=7281$, and $99^{2}=9801$. Since $7281
eq9801$, these do not form a right - triangle.
- For $11$, $85$, $99$:
$11^{2}+85^{2}=121+7225 = 7346$, and $99^{2}=9801$. Since $7346
eq9801$, these do not form a right - triangle.
- For $13$, $85$, $99$:
$13^{2}+85^{2}=169+7225 = 7394$, and $99^{2}=9801$. Since $7394
eq9801$, these do not form a right - triangle.
- For $84$, $85$, $99$:
$84^{2}+85^{2}=7056+7225 = 14281$, and $99^{2}=9801$. Since $14281
eq9801$, these do not form a right - triangle.

# Answer:
The side lengths $13$ feet, $84$ feet, and $85$ feet can form a right - triangle.

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the Pythagorean theorem

Step2: Check each combination

Answer: