Questions: Given trapezoid ABCD with AB perpendicular to DC; also, M and N are midpoints of AD and BC respectively. Given: AB=8.2 and MN=12.4. Find DC.

Transcript text: Given trapezoid $A B C D$ with $A B \perp D C$; also, $M$ and $N$ are midpoints of $A D$ and $B C$ respectively. Given: $A B=8.2$ and $M N=12.4$. Finds DC.

Solution

Solution Steps

Step 1: Applying the Trapezoid Midsegment Theorem

The trapezoid midsegment theorem states that the length of the midsegment (MN) is equal to the average of the lengths of the two parallel bases (AB and DC). Therefore, MN = (AB + DC)/2.

Step 2: Substituting Given Values

We are given that AB = 8.2 and MN = 12.4. Substituting these values into the equation from Step 1 gives us: 12.4 = (8.2 + DC)/2.

Step 3: Solving for DC

Multiply both sides of the equation by 2: 24.8 = 8.2 + DC. Subtract 8.2 from both sides of the equation: DC = 24.8 - 8.2 Simplify: DC = 16.6