find the length of the longest side of the triangle formed by the line 3x+4y=12 with the coordinate axes
Answers
Given line is 3x+4y=12
First we find the points where the line meets coordinate axes
put y=0, we get
3x=12
x=4
put x=0, we get
4y=12
y=3
The given line meets
the coordinate axes at (4,0) and (0,3)
The length of the longest side of the triangle formed by the line 3x+4y=12
= The distance betweeen (4,0) and (0,3)
The longest side has length 5 units.
Step-by-step explanation:
- This question can be solved in the easiest manner, by using the equation of intercept form of line.
We know that:
- Equation for intercept form of line :
Where; 'a' is the x - intercept.
'b' is the y - intercept.
We are given the equation of line as;
- 3x + 4y = 12
We try to convert it in the intercept form. We divide both the sides, by 12.
Now, x - intercept is 4 and y - intercept is 3.
- Since, the triangle is the right angle triangle.
- We can apply Pythagoras theorem.
, since it is length. So it can't be negative.
Therefore; AB = 5 units
This is the longest side of the triangle.
Thus, the longest side has length 5 units.