Δabc is a right triangle. δa'b'c' has a hypotenuse of 10 after δabc undergoes a dilation by a factor of 2. if δabc has a short leg of 5 - x and a long leg of 2x, what is the length of the short leg of δabc?

Since the ΔABC is a dilation of the first triangle by 2, the hypotenuse of this new triangle is equal to 20. By Pythagorean theorem,
                                      hypotenuse² = (shorter leg)² + (longer leg)²
Substituting the given expression for each of the leg
                                       20² = (5 - x)² + (2x)²
The value of x from the equation is -7.71. The shorter leg is 5 - x which is equal to 12.71. 

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