We develop two equations based on the given diagram. We let x be the length from C to the point meeting the endpoint of 5. We let y be the length of CD.
First, we determine the length from D to the endpoint of line measuring 9 cm. We use the Pythagorean theorem.
l = sqrt ((3)² + 5²)
l = 5.83
Then, the equations that can be developed or established are:
x² + 6² = y²
9² + (5 + x)² = (y + 5.83)²
In solving for x and y, we use substitution.
From the first equation,
y = sqrt (x² + 36)
We substitute this to the second equation y.
The value of x is 9.51.
y = sqrt (9.51² + 36) = 11.25.
Calculate for the area of the bigger triangle.
A = 0.5(9 cm)(5 + 9.51 cm) = 65.295 cm²
Also calculate for the area of the smaller triangle,
A = (0.5)(6 cm)(9.51 cm) = 28.53 cm²
The difference between the areas is 36.765 cm².
ANSWER: 36.77 cm²
