Question

find the length of the missing leg. a. 4 m b. 16 m c. 28 m d. 32 m

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. Let the missing leg be \(x\). Given \(c = 100\) m and one leg \(a=96\) m. Then \(x^{2}+96^{2}=100^{2}\).

Step2: Rearrange the formula

\(x^{2}=100^{2}-96^{2}\). Using the difference of squares \(A^{2}-B^{2}=(A + B)(A - B)\), here \(A = 100\) and \(B=96\). So \(x^{2}=(100 + 96)(100 - 96)\).
\(x^{2}=(196)\times(4)\).
\(x^{2}=784\).

Step3: Solve for \(x\)

Take the square root of both sides. \(x=\sqrt{784}\).
\(x = 28\) m.

Answer:

C. 28 m