Question

betty would like to construct a right triangle. the lengths of the hypotenuse and one of the legs are 34 and 30 inches, respectively. what is the length of the other leg?
a 4 inches
b 8 inches
c 16 inches
d 64 inches

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 30\), \(c=34\), and \(b\) be the unknown leg. The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

Substitute \(a = 30\) and \(c = 34\) into \(b^{2}=c^{2}-a^{2}\). Then \(b^{2}=34^{2}-30^{2}=(34 + 30)(34 - 30)\) (using \(x^{2}-y^{2}=(x + y)(x - y)\)).
\(b^{2}=(64)\times(4)=256\).

Step3: Solve for \(b\)

Take the square root of \(b^{2}=256\). Since \(b>0\) (length of a side), \(b=\sqrt{256}=16\).

Answer:

C. 16 inches