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 cm 2√2 cm 4 cm 4√2 cm

Explanation:

Step1: Calculate hypotenuse length

For an isosceles right - triangle with leg \(a = 4\text{ cm}\), by Pythagorean theorem \(c=\sqrt{a^{2}+a^{2}}\). Substitute \(a = 4\), \(c=\sqrt{4^{2}+4^{2}}=\sqrt{16 + 16}=\sqrt{32}=4\sqrt{2}\text{ cm}\).

Step2: Use area formula

Area of a right - triangle \(S=\frac{1}{2}\times a\times a\) (using legs) and also \(S=\frac{1}{2}\times c\times h\) (using hypotenuse \(c\) and altitude \(h\)).
Since \(S=\frac{1}{2}\times4\times4 = 8\text{ cm}^2\) and \(S=\frac{1}{2}\times4\sqrt{2}\times h\).
Set \(\frac{1}{2}\times4\sqrt{2}\times h=8\), solve for \(h\):

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Answer:

B. \(2\sqrt{2}\text{ cm}\)