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

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be $b$. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 26$ (hypotenuse) and $a = 10$. So $b=\sqrt{c^{2}-a^{2}}=\sqrt{26^{2}-10^{2}}$.

Step2: Calculate the value of $b$

$b=\sqrt{(26 + 10)(26 - 10)}=\sqrt{36\times16}=\sqrt{576}=24$ km.

Step3: Calculate the perimeter $P$

$P=a + b + c=10+24 + 26=60$ km.

Step4: Calculate the area $A$

The area of a right - triangle is $A=\frac{1}{2}\times\text{base}\times\text{height}=\frac{1}{2}\times10\times24 = 120$ $km^{2}$.

Answer:

a. 24 km
b. 60 km
c. 120 $km^{2}$