ABCD is a trapezoid with median EF and bases AB and CD. AB = 18, EF = 28. Find CD
Length of CD would be 26.
If AB=2×+10,DC=3×+20 and LM=4×,what is LM
To find CD, we need to understand the properties of a trapezoid and its median.
In a trapezoid, the bases are parallel to each other. The median EF is a line segment that connects the midpoints of the legs of the trapezoid, in this case, AB and CD.
Given that AB = 18 and EF = 28, we can use the properties of a trapezoid to solve for CD.
The ratio of the lengths of the bases of a trapezoid is equal to the ratio of the lengths of the medians. In other words, if AB and CD are the bases, and EF and GH are the medians (where GH connects the midpoints of AD and BC), then the ratio of AB to CD is equal to the ratio of EF to GH.
Mathematically, we can express this as:
AB/CD = EF/GH
Since EF and GH are medians, they intersect each other at a point, dividing each other in half. Therefore, GH = EF = 28.
Substituting the given values, we have:
18/CD = 28/28
Simplifying the equation, we get:
18/CD = 1
Now, cross-multiply:
18 = CD
So, CD = 18.
Therefore, CD is equal to 18 in this trapezoid.