Question

The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is:
A. 8
B. 10
C. 12
D. 15

Answer 1

Hint: Here, mark the points on the graph, and join the lines to form a triangle. Using distance formula, find the length of three sides. Add the three lengths to find the perimeter of the triangle.

Complete step-by-step answer:
Let the points are A (0, 4), O (0, 0) and B (3, 0).

For length OA,
Using distance formula,
 $ \Rightarrow OA = \sqrt {{{(0 - 0)}^2} + {{(4 - 0)}^2}} = \sqrt {16} = 4 $ units
For length OB,ss
Using distance formula,
 $ \Rightarrow OB = \sqrt {{{(3 - 0)}^2} + {{(0 - 0)}^2}} = \sqrt 9 = 3 $ units
For length AB,
Using distance formula,
 $ \Rightarrow AB = \sqrt {{{(0 - 3)}^2} + {{(4 - 0)}^2}} = \sqrt {9 + 16} = \sqrt {25} = 5 $ units
Perimeter of triangle ABC, $ P = AB + BC + AC $
P = 3 units + 4 units + 5 units = 12 units
So, the correct answer is “12 units”.

Note: In these types of questions, draw the figure on a graph to understand the question geometrically.One important thing about this question is that we can find hypotenuse using Pythagoras theorem as one angle in this question is right angle. Here, (0, 4) means length of this point from origin is 4 units and (3, 0) means length of this point from the origin is 3 units. Using these two lengths and Pythagoras theorem we can find the length of the third side. Add them to get the perimeter of the triangle.