A right triangle has sides 5, 12, and 13. A smaller similar triangle is inscribed with a perimeter of 10. What is its area?

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Accepted Answer

1. Original triangle: perimeter $P=5+12+13=30$. Area $A=	frac{1}{2}\cdot5\cdot12=30$.
2. The smaller triangle is similar, so scale $s=\dfrac{10}{30}=	frac{1}{3}$.
3. Area scales by $s^2$. So $A_{small}=30\left(	frac{1}{3}ight)^2=	frac{10}{3}$.
4. $	frac{10}{3}\approx3.33$. Thus choice **(b)** is correct.
FINAL_ANSWER: b

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