posted by Jen .
Find the perimeter and area of a right triangle if the shortest side is 20 mm. and the longest side is 52 mm.
See later post.
The shortest side, we are told, is 20mm. This is one of the 'legs' of the right triangle, adjacent to the right angle.
We are told that the longest side is 52mm. This by definition is the hypotenuse (the side OPPOSITE the right angle). Hence the side we are trying to find the length of is the other 'leg' which has intermediate value.
Using Pythagoras' Theorem, and allowing the unknown 'base/ leg' be x:
(20)^2 + (x)^2 = (52)^2
or (4000 + (x^2) = (2704)
implying x = 48mm after simplification, etc..
The Perimeter, therefore, is (20+48+52)mm = 120mm.
The area , therefore, is = 1/2 * base * perp. height
Area = 1/2 * 48 * 20 = 480 mm^2.