an isosceles trapesiod has legs that measure 24 units each. If the perimeter of the trapeziod is 150 units, what is the legth of its median?.
24+24 = 48
150-48 = 102
so top + bottom = 102
average of top and bottom = median = 51
To find the length of the median of an isosceles trapezoid, we need to understand that the median is the line segment that connects the midpoints of the two bases. In an isosceles trapezoid, the bases are the parallel sides of unequal length.
In this case, we know that the length of the legs (non-parallel sides) of the trapezoid is 24 units each. Let's use this information to find the length of the shorter base.
Since the trapezoid is isosceles, we can assume that the length of the shorter base is 'x' units. Therefore, the length of the longer base would also be 'x' units.
Now, we can calculate the perimeter of the trapezoid by adding up all the sides:
Perimeter = Length of Shorter Base + Length of Longer Base + 2 × Leg Length
150 = x + x + 2 × 24
150 = 2x + 48
Subtracting 48 from both sides:
102 = 2x
Dividing both sides by 2:
x = 51
Now that we know the length of the shorter base (51 units), we can find the length of the median.
The median is the average of the lengths of the two bases. So, to find the length of the median, we add the lengths of the bases and divide by 2:
Median = (Length of Shorter Base + Length of Longer Base) / 2
Median = (51 + 51) / 2
Median = 102 / 2
Median = 51 units
Therefore, the length of the median of the isosceles trapezoid is 51 units.