A right triangle is formed by the origin and the x and y intercepts of the line 14x+7y=56. Find the area of the triangle.
I know that Area of a triangle is 1/2bh, but how do I find the base and height? Thank you.
I found x=4 and y=8 is that right? Then I found the area is 16. Is that right?
base is 4
altitude is 8
x and y axes hit each other at the origin at 90 degrees (360/4)
area is 16
Yay! Thank you!
To find the area of the right triangle formed by the origin and the x and y intercepts of the line 14x + 7y = 56, we need to first find the coordinates of the x and y intercepts.
To find the x-intercept, set y = 0 and solve for x:
14x + 7(0) = 56
14x = 56
x = 56/14
x = 4
So, the x-intercept is (4, 0).
To find the y-intercept, set x = 0 and solve for y:
14(0) + 7y = 56
7y = 56
y = 56/7
y = 8
So, the y-intercept is (0, 8).
Now that we have the coordinates of the x and y intercepts, we can use these points to calculate the base and height of the triangle.
The base of the triangle is the distance between the x-intercept (4, 0) and the origin (0, 0), which is simply the x-coordinate of the x-intercept, which is 4.
The height of the triangle is the distance between the y-intercept (0, 8) and the origin (0, 0), which is simply the y-coordinate of the y-intercept, which is 8.
Now that we have the base and height of the triangle, we can plug them into the formula for the area of a triangle: Area = 1/2 * base * height.
Area = 1/2 * 4 * 8 = 16
Therefore, the area of the right triangle formed by the origin and the x and y intercepts of the line 14x + 7y = 56 is 16 square units.