Final answer:
To find the length of x in △ABC, we can use the fact that △ABC is similar to △DEC. By setting up a proportion using the length of sides AB and DE, we can solve for x and find that its length is 0.
Step-by-step explanation:
To find the length of x in △ABC, we can use the fact that △ABC is similar to △DEC. According to the given information, the length of side x in △ABC is m. Since △ABC and △DEC are similar, their corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides in the two triangles is the same.
So, if we let the length of side DE be n, then the ratio of x to n is the same as the ratio of AB to DE. This can be written as:
x/n = AB/DE
Since we are trying to find the length of x, we can rearrange the equation to solve for x:
x = (AB/DE) × n
Now, we know that AB = 3x, so we can substitute this into the equation:
x = (3x/DE) × n
Given that AB = 3x and DE = n, we can simplify the equation further:
x = (3x/n) × n
Next, we can cross multiply:
x × n = 3x × n
Finally, we can cancel out the common factor of n:
x = 3x
x - 3x = 0
-2x = 0
x = 0
Therefore, the length of x is 0.