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 ___

b. the perimeter of the triangle is ___

c. the area of the triangle is ___

Answer 1

Answer:

(A) 40 km

(B) 90 km

(C) 180 km²

Step-by-step explanation:

To find the missing side of this triangle, let's use the Pythagorean theorem.

$a^2+b^2=c^2$, assuming that a and b are legs, and c is the hypotenuse.

Assuming the 9km side is a, we need to find the value of b, so we can substitute into the equation.

$9^2+b^2=41^2\\81+b^2=1681\\b^2=1681-81\\b^2=1600\\\\b = \sqrt{1600} \\b=40$

So, the length of the missing side is 40. Now that we know this piece of information, we can find the perimeter and area of the triangle.

The perimeter is all the sides added together, so $41+9+40 = 90$ km is the perimeter.

The area are the two legs multiplied divided by 2.

So,

$\frac{9\cdot40}{2} \\\\\frac{360}{2}\\\\180$

So the area of this triangle is 180 cm²

I hope this helped!