Answer:
Explanation:
Compare both shapes
Find out the length of the red line through Pythagoras theorem
a² + b² = c²
9² + b² = 15²
15²- 9² = b²
144 = b²
√144 = b
b = 12
Red line is 12 and the other length of one side of the triangle is x - 9
The hypotenuse of the other triangle will be equal to:
a² + b² = c²
12² + (x-9)² = c²
144 + x² - 9x -9x + 81 = c²
x² - 18x + 225 = c²
THE HYPOTENUSE OF THE 2ND TRIANGLE = x² - 18x + 225
NOW COMPARE BOTH TRIANGLES
x² - 18x + 225 : 15
x - 9 : 9
Cross multiply
9(x² - 18x + 225) = 15(x - 9)
9x² - 162x + 2025 = 15x - 135
9x² - 162x - 15x + 2025 + 135 = 0
9x² - 177x + 2160 = 0
Now use the quadratic equation
x = (-b +- √b² - 4ac)/2a
a = 9
b = -177
c = 2160
x = (-(-177) +- √(-177)² - 4(9)(2160))/(2×9)
x = (177 +- √31329 - 77760)/(18)
x = (177 +- √-46431)/18
At this point I have lost hope in the question as i got a negative value under square root which means it can't be solved.
I don't know where I am wrong but I hope the starting parts of the answer help you reach the final answer.