Geometry

Rectangle ABCD has sides AB = 32 yd and BC = 26 yd. Find CD and AD.

Step-by-step solution with explanation

Final Answer

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Step-by-step solution

1

Sketch and label the rectangle

Draw rectangle ABCD with vertices in order. Label the known sides so we can see which sides are opposite each other.
2

Use opposite sides are equal

In any rectangle, opposite sides are equal in length. AB is opposite to CD, and BC is opposite to AD.
3

Substitute the known values

Plug in AB = 32 yd to get CD, and plug in BC = 26 yd to get AD. That gives us both missing sides.

Understanding this problem

Learning Insight

A rectangle is a special parallelogram, and parallelograms always have two pairs of opposite sides that are exactly equal. This comes from the definition: both pairs of opposite sides are parallel and congruent.

Quick Tip

In a rectangle ABCD listed in order, just remember: side 1 = side 3, and side 2 = side 4. AB matches CD, BC matches AD — every time.

Common Mistake

Students sometimes match adjacent sides instead of opposite sides, thinking AB = BC or CD = AD, which is only true for a square.