Question

message abcd is a side showing of the rectangular part of a shed to be built. angled cd is 8 feet and opposite side from is 15 feet and ad is 6 feet. what is the length in feet of the side of the floor represented by ad?
a 8
b 0
c 14
d 10
e 18

Explanation:

Step1: Use the Pythagorean theorem

Let the length of \(AD\) be \(x\). Assume \(CD = 16\) (since it's mentioned as a side), and the other side is \(12\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), here \(x=\sqrt{16^{2}-12^{2}}\).

Step2: Calculate the value

First, \(16^{2}=256\) and \(12^{2} = 144\). Then \(16^{2}-12^{2}=256 - 144=112\). Wait, no! Wait, if it's a right - angled triangle (assuming the figure is a right - angled triangle as it's about a side of a tent floor), if the hypotenuse is \(16\) (maybe a mis - read, if the problem is about a right - angled triangle with legs \(12\) and \(x\) and hypotenuse \(20\) (another assumption, since if we consider Pythagorean triples \(12 - 16-20\) where \(a = 12\), \(b=16\), \(c = 20\) is wrong. Wait, no! Wait, if we assume that the problem is a right - angled triangle and one side is \(12\) (maybe the mis - written \(AD = 12\) was a typo, and we use \(a^{2}+b^{2}=c^{2}\), if \(c = 20\) (hypotenuse) and \(a = 12\), then \(b=\sqrt{20^{2}-12^{2}}=\sqrt{(20 + 12)(20 - 12)}=\sqrt{32\times8}=\sqrt{256}=16\). No, wrong approach. Wait, re - reading: If it's a right - angled triangle (tent floor is often rectangular, but if we consider a right - angled sub - part). Wait, standard Pythagorean triple \(6-8 - 10\). If one side is \(6\) (maybe \(AD = 6\) is a mis - print, no. Wait, another approach: Assume the problem is a right - angled triangle. Let's use \(a^{2}+b^{2}=c^{2}\). If \(c = 10\) (hypotenuse) and \(a=6\), then \(b=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8\).

Answer:

A. 8