Question

if the legs of an isosceles right triangle have a length of (15\sqrt{2}\\) ft, what is the length of the hypotenuse?

7.5 feet
(15\sqrt{2}\\) feet
(15\sqrt{3}\\) feet
30 feet

Explanation:

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<reasoning>

Identify the given values and formula

\[

$$\begin{aligned} &\text{Leg length } (a) = 15\sqrt{2}\text{ ft}\\ &\text{Hypotenuse } (c) = a\sqrt{2} \end{aligned}$$

\]

Calculate the hypotenuse length

\[

$$\begin{aligned} c &= (15\sqrt{2}) \cdot \sqrt{2} \\ c &= 15 \cdot 2 \\ c &= 30\text{ feet} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 7.5 feet</mcq-option>
<mcq-option>(B) \(15\sqrt{2}\) feet</mcq-option>
<mcq-option>(C) \(15\sqrt{3}\) feet</mcq-option>
<mcq-correct>(D) 30 feet</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Geometry",
"Isosceles Right Triangle Properties"
]
}
</post_analysis>

Answer:

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<reasoning>

Identify the given values and formula

\[

$$\begin{aligned} &\text{Leg length } (a) = 15\sqrt{2}\text{ ft}\\ &\text{Hypotenuse } (c) = a\sqrt{2} \end{aligned}$$

\]

Calculate the hypotenuse length

\[

$$\begin{aligned} c &= (15\sqrt{2}) \cdot \sqrt{2} \\ c &= 15 \cdot 2 \\ c &= 30\text{ feet} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) 7.5 feet</mcq-option>
<mcq-option>(B) \(15\sqrt{2}\) feet</mcq-option>
<mcq-option>(C) \(15\sqrt{3}\) feet</mcq-option>
<mcq-correct>(D) 30 feet</mcq-correct>
</answer>

<post_analysis>
{
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"Geometry",
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