AMC12 2015 A

AMC12 2015 A · Q2

AMC12 2015 A · Q2. It mainly tests Triangles (properties).

Two of the three sides of a triangle are 20 and 15. Which of the following numbers is not a possible perimeter of the triangle?

一个三角形的三个边中有两条分别是 20 和 15。以下哪个数不可能是该三角形的周长？

(A) 52 52

(B) 57 57

(D) 67 67

(E) 72 72

Answer

Correct choice: (E)

正确答案：（E）

Solution

By the Triangle Inequality the third side must be greater than $20 - 15 = 5$ and less than $20 + 15 = 35$. Therefore the perimeter must be greater than $5 + 20 + 15 = 40$ and less than $35 + 20 + 15 = 70$. Among the choices only 72 cannot be the perimeter.

根据三角不等式，第三条边必须大于 $20 - 15 = 5$ 且小于 $20 + 15 = 35$。因此周长必须大于 $5 + 20 + 15 = 40$ 且小于 $35 + 20 + 15 = 70$。选项中只有 72 不可能是周长。

Topics

GE.002 Triangles (properties)