A rectangle has a side that is 10 units long. How long will this side be after the figure us translated down 4 units and to there's right 5 units?
After the rectangle is translated down 4 units, the length of this side will still be 10 units. Translating the rectangle 5 units to the right will not affect the length of this side. Therefore, the length of this side will remain 10 units after the translation.
To find the length of the side after the translation, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
In this case, the side of the rectangle is the hypotenuse, and the downward translation of 4 units and the rightward translation of 5 units are the other two sides.
Using the Pythagorean theorem, we can find the length of the side after the translation:
Length after translation = √(10² + 4² + 5²)
= √(100 + 16 + 25)
= √(141)
≈ 11.87 units (rounded to two decimal places)
Therefore, the side will be approximately 11.87 units long after the figure is translated down 4 units and to the right 5 units.