The value of m is 15
How to determine the value of m.
From the figure
3/12 = 5/5+m
Solving for m in the equation 3/12 = 5/5+m
Cross-multiply to eliminate fractions:
3(5+m) = 12 * 5
Distribute and simplify:
15 + 3m = 60
Subtract 15 from both sides:
3m = 45
4. Divide by 3:
m = 15
Therefore, m = 15
Or
Using Pythagorean theorem
(5+m)² = 12² + 16²
Expand the left side:
(5+m)² = (5+m)(5+m) = 25 + 10m + m²
Set up the equation:
25 + 10m + m^2 = 12² + 16²
Simplify the right side:
25 + 10m + m² = 144 + 256
Combine like terms:
m² + 10m + 25 = 400
Subtract 400 from both sides:
m² + 10m - 375 = 0
Factor or use the quadratic formula to find m.
(m + 25)(m - 15) = 0
m + 25 = 0 , m = -25
m - 15 = 0 , m = 15
The value of m cannot be negative, therefore m = -25 is invalid.
The value of m is 15