AMC12 2007 A

AMC12 2007 A · Q10

AMC12 2007 A · Q10. It mainly tests Pythagorean theorem, Area & perimeter.

A triangle with side lengths in the ratio $3 : 4 : 5$ is inscribed in a circle with radius 3. What is the area of the triangle?

一个边长比为 $3 : 4 : 5$ 的三角形内接于半径为 3 的圆中。该三角形的面积是多少？

(A) 8.64 8.64

(B) 12 12

(D) 17.28 17.28

(E) 18 18

Answer

Correct choice: (A)

正确答案：（A）

Solution

Error creating thumbnail: Unable to save thumbnail to destination Since 3-4-5 is a Pythagorean triple, the triangle is a right triangle. Since the hypotenuse is a diameter of the circumcircle, the hypotenuse is $2r = 6$. Then the other legs are $\frac{24}5=4.8$ and $\frac{18}5=3.6$. The area is $\frac{4.8 \cdot 3.6}2 = 8.64\ \mathrm{(A)}$

由于 3-4-5 是勾股数组，该三角形是直角三角形。因为斜边是外接圆的直径，所以斜边长为 $2r = 6$。则两条直角边分别为 $\frac{24}5=4.8$ 和 $\frac{18}5=3.6$。面积为 $\frac{4.8 \cdot 3.6}2 = 8.64\ \mathrm{(A)}$

Topics