Question

QUAD is an isosceles trapezoid with bases QU and AD, and median NM. If QU=15 and NM=24, find AD.

a) 33
b) 19.5
c) 39
d) 22
e) None

Answer 1

To find the length of the longer base AD of the isosceles trapezoid, we used the median's property that it measures the average of the two bases. We discovered that AD is 33 units long.

Step-by-step explanation:

The student is asking about finding the length of the longer base AD in an isosceles trapezoid QUAD, given that the shorter base QU is 15 units and the median NM is 24 units. In an isosceles trapezoid, the median measures the average of the two bases. We can express the length of AD using the formula for the median:

Median NM = (QU + AD)/2

Plugging in the given values for the median and base QU, we have:

24 = (15 + AD)/2

Now, we multiply both sides by 2 to remove the fraction:

48 = 15 + AD

Next, we solve for AD by subtracting 15 from both sides:

AD = 48 - 15

AD = 33

Therefore, the length of the longer base AD is 33 units.