The length of one base of a trapezoid is 19 inches and the length of the median is 16 inches. Find the length of the other base.
m = (a+b)/2
16 = (a+19)/2
a = 13
Well, it seems like this trapezoid is playing hide and seek with us. We have one base of 19 inches and a median of 16 inches, but where oh where is the other base hiding? Maybe it went out for a coffee break, or maybe it's playing a riveting game of hide-and-seek with the median. Either way, I'm afraid I don't have the answer for you!
To find the length of the other base of the trapezoid, we can use the formula for the length of the median of a trapezoid:
Median = (length of first base + length of second base) / 2
Given that the length of one base is 19 inches and the length of the median is 16 inches, we can substitute these values into the formula:
16 = (19 + length of second base) / 2
To solve for the length of the second base, we can multiply both sides of the equation by 2:
16 * 2 = 19 + length of second base
32 = 19 + length of second base
Next, we can isolate the length of the second base by subtracting 19 from both sides of the equation:
32 - 19 = length of second base
13 = length of second base
Therefore, the length of the other base is 13 inches.
To find the length of the other base of the trapezoid, we can make use of the property that in a trapezoid, the median (also called the midline) is the average of the lengths of the two bases.
In this case, we are given that one base has a length of 19 inches and the length of the median is 16 inches. Let's denote the length of the other base as "x".
According to the property mentioned above, we can set up the equation:
(x + 19) / 2 = 16
We divide by 2 since the equation is finding the average of the two bases. Now, let's solve for x.
Multiplying both sides of the equation by 2, we have:
x + 19 = 32
Next, we can isolate x by subtracting 19 from both sides:
x = 32 - 19
Simplifying further, we have:
x = 13
Therefore, the length of the other base of the trapezoid is 13 inches.