Geometry

Rectangle EFGH with FG = 34 yd and HG = 52 yd. Find EH and EF.

Step-by-step solution with explanation

Final Answer

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Step-by-step solution

1

Label the rectangle sides clearly

We start by identifying the given side lengths. In rectangle EFGH, vertices go in order, so opposite sides are equal and all angles are 90°.
2

Identify opposite side pairs

In any rectangle, opposite sides are equal in length. EH is opposite to FG, and EF is opposite to HG.
3

Set EH equal to opposite side FG

Since EH and FG are opposite sides of the rectangle, they must be the same length.
4

Set EF equal to opposite side HG

Since EF and HG are opposite sides of the rectangle, they must be the same length.

Understanding this problem

Learning Insight

A rectangle is defined as a parallelogram with four right angles. In every parallelogram, opposite sides are parallel AND equal in length. That's why you can always find a missing side by looking at the side directly across from it.

Quick Tip

Label the vertices in order (E→F→G→H) and draw a quick sketch. The side you want is always directly across from the side you already know — no math needed beyond matching pairs!

Common Mistake

Students often confuse adjacent sides with opposite sides, matching EH with HG (which share vertex H) instead of matching EH with FG. Always check that the two sides you're comparing are truly across from each other, not next to each other.