Question

1. a right triangle has a hypotenuse that is √80 units long. which choice shows possible measures of the legs of the triangle? a 4 units and 5 units b. 4 units and 8 units c. 5 units and 10 units d. 8 units and 10 units

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a,b\) are the legs. Given \(c = \sqrt{80}\), then \(c^{2}=80\).

Step2: Check each option

• Option A:

If \(a = 4\) and \(b = 5\), then \(a^{2}+b^{2}=4^{2}+5^{2}=16 + 25=41
eq80\).

• Option B:

If \(a = 4\) and \(b = 8\), then \(a^{2}+b^{2}=4^{2}+8^{2}=16+64 = 80\).

• Option C:

If \(a = 5\) and \(b = 10\), then \(a^{2}+b^{2}=5^{2}+10^{2}=25 + 100=125
eq80\).

• Option D:

If \(a = 8\) and \(b = 10\), then \(a^{2}+b^{2}=8^{2}+10^{2}=64+100 = 164
eq80\).

Answer:

B. 4 units and 8 units