Question

(a) use the pythagorean theorem to determine the length of the unknown side of the triangle, (b) determine the perimeter of the triangle, and (c) determine the area of the triangle. the figure is not drawn to scale. a. the length of the unknown side is (type a whole number).

Explanation:

Step1: Apply Pythagorean theorem

Let the two legs of the right - triangle be $a = 12$ yd and $b = 16$ yd, and the hypotenuse be $c$. The Pythagorean theorem is $c^{2}=a^{2}+b^{2}$. So $c=\sqrt{12^{2}+16^{2}}=\sqrt{144 + 256}=\sqrt{400}=20$ yd.

Step2: Calculate the perimeter

The perimeter $P$ of a triangle is the sum of the lengths of its sides. So $P=12 + 16+20=48$ yd.

Step3: Calculate the area

The area $A$ of a right - triangle is given by $A=\frac{1}{2}\times\text{base}\times\text{height}$. Here, the base can be 12 yd and the height can be 16 yd. So $A=\frac{1}{2}\times12\times16 = 96$ yd².

Answer:

a. 20 yd
b. 48 yd
c. 96 yd²