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.
the length of the unknown side is ____

the perimeter of the triangle is ____

the area of the triangle is ___

Answer 1

Answer/Step-by-step explanation:

a. Unknown side, b, using the Pythagorean theorem is solved as shown below.

$b^2 = c^2 - a^2$

$b^2 = 45^2 - 27^2$

$b^2 = 1,296$

$b = \sqrt{1,296}$

$b = 36$

Unknown side, b, = 36 km

b. Perimeter of the triangle = sum of all the sides of the ∆ = $36 + 45 + 27$

$perimeter = 108 km$

c. Area of triangle = ½*base*height

where,

Base = 36 km

Height = 27 km

$Area = \frac{1}{2}*36*27$

$Area = 18*27$

$Area = 486 km^2$