Question 404·Easy·Math

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In a right triangle, one leg measures $6$ inches and the hypotenuse measures $10$ inches. What is the length of the triangle's other leg, in inches?

A Pythagorean triple is a set of whole-number side lengths for a right triangle. If the given leg and hypotenuse match two sides of a familiar triple, find their shared scale factor and apply it to the missing side. The hypotenuse is the longest side; subtracting the two given lengths does not find the other leg.

Hints

Hint 1
The hypotenuse is the side across from the right angle. In the familiar $3$ - $4$ - $5$ right triangle, $5$ is the hypotenuse. How could you scale $5$ to match the hypotenuse here?
Hint 2
A scale factor multiplies every side of a triangle by the same number. Compare $3$ with $6$ and $5$ with $10$ . What must happen to the remaining side?

Step-by-step

Scale a familiar right triangle
Step 1
Match the given sides to a triple
No Desmos needed. The side lengths match a familiar right-triangle pattern. The Pythagorean triple $3$ - $4$ - $5$ has legs $3$ and $4$ and hypotenuse $5$ . Here, $10$ is the hypotenuse: $6=2\times3$ and $10=2\times5$ . So this triangle is twice the size of the $3$ - $4$ - $5$ triangle.
Step 2
Scale the missing leg
Multiply every side by the same scale factor. The missing leg corresponds to $4$ , so multiply it by $2$ :
$4\times2=8.$
The other leg is $8$ inches. Choice B.

Lessons that teach this

SAT Geometry and TrigonometryBeginnerCoreApply the Pythagorean theorem

Question 404·Easy·Math

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Step-by-step

Lessons that teach this

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Strategy

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Step-by-step

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