Algebra-2

Step 1: Express the intercepts in terms of a, b, and c
The x-intercept occurs where y = 0, so the x-intercept is:

x-intercept=(c/a,0)

The y-intercept occurs where x = 0, so the y-intercept is:

y-intercept=(0,c/b)

Step 2: Use the given information about the sum of intercepts
We know the sum of the intercepts is 10: c/a + c/b = 7

Factor out c on the left side: c(1/a + 1/b) = 7.

Step 3: Use the given information about the area of the triangle
The area of the triangle formed by the line and the coordinate axes is given by:

Area = 1/2 × x-intercept × y-intercept = 6

Substitute the intercepts: 1/2 × c/a × c/b = 6

Simplify the equation: c²/2ab = 12 ⇒ c² = 12ab
...