Question 524·Easy·Math

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In right triangle $\triangle DEF$ , angle $E$ is the right angle. If the lengths of the sides are $DE = 5$ centimeters and $DF = 13$ centimeters, what is the length of side $EF$ , in centimeters?

A right angle cues the Pythagorean theorem: the squares of the two sides touching that angle add to the square of the side across from it. First identify which side is across from the right angle. If the given lengths fit a familiar whole-number triple, you can use it to find the missing side quickly. Don't subtract the side lengths themselves; the theorem relates their squares.

Hints

Hint 1
The hypotenuse is the side across from the right angle, and it's the longest side. Look across from angle $E$ : which given side is the hypotenuse?
Hint 2
A Pythagorean triple is a set of three whole-number side lengths that fit a right triangle. The missing side is a leg, not the hypotenuse. Do the given lengths remind you of a familiar triple?

Step-by-step

Use a familiar right-triangle triple
Step 1
Identify the hypotenuse
No Desmos needed. These lengths fit a familiar right-triangle triple. Because angle $E$ is the right angle, $DF$ is across from the right angle. So $DF=13$ is the hypotenuse, the longest side. $DE=5$ and the requested side $EF$ are the two legs that meet at $E$ .
Step 2
Match the triple to the missing leg
The familiar Pythagorean triple $5,12,13$ fits because $5^2+12^2=13^2$ . Its hypotenuse is $13$ , and its legs are $5$ and $12$ . Here $DE$ is the $5$ -centimeter leg, so the other leg is $12$ . Side $EF$ measures $12$ centimeters. Choice B.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreApply the Pythagorean theorem

Question 524·Easy·Math

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Step-by-step

Lessons that teach this

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Strategy

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