an isosceles right triangle has leg lengths of 4 centimeters. what is the length of the altitude drawn from the right angle to the hypotenuse?

$2\text{ cm}$
$2\sqrt{2}\text{ cm}$
$4\text{ cm}$
$4\sqrt{2}\text{ cm}$

Question

an isosceles right triangle has leg lengths of 4 centimeters. what is the length of the altitude drawn from the right angle to the hypotenuse?

$2\text{ cm}$
$2\sqrt{2}\text{ cm}$
$4\text{ cm}$
$4\sqrt{2}\text{ cm}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Pythagorean Theorem", "Right Triangle Altitude" ], "new_concepts": [ "Isosceles Right Triangle Properties" ], "current_concepts": [ "Pythagorean Theorem", "Right Triangle Altitude", "Isosceles Right Triangle Properties" ] } ## Calculate the hypotenuse length $$ \begin{aligned} a &= 4\text{ cm},\quad b = 4\text{ cm}\ c &= \sqrt{a^2 + b^2} = \sqrt{4^2 + 4^2} = \sqrt{32} = 4\sqrt{2}\text{ cm} \end{aligned} $$ ## Calculate the altitude to the hypotenuse $$ \begin{aligned} \text{Area} &= \frac{1}{2} \cdot a \cdot b = \frac{1}{2} \cdot 4 \cdot 4 = 8\text{ cm}^2\ \text{Area} &= \frac{1}{2} \cdot c \cdot h \implies 8 = \frac{1}{2} \cdot 4\sqrt{2} \cdot h\ h &= \frac{16}{4\sqrt{2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2}\text{ cm} \end{aligned} $$

$2\text{ cm}$

$2\sqrt{2}\text{ cm}$

$4\text{ cm}$

$4\sqrt{2}\text{ cm}$

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QUESTION IMAGE

Question

Explanation:

Calculate the hypotenuse length

Calculate the altitude to the hypotenuse

Answer: