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?

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08-02-2017
Mathematics

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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?

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taskmasters taskmasters · Answer 1 · 2017-02-10T17:28:49+01:00

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.