AMC10 2013 A

AMC10 2013 A · Q3

AMC10 2013 A · Q3. It mainly tests Area & perimeter.

Square $ABCD$ has side length 10. Point $E$ is on $\overline{BC}$, and the area of $\triangle ABE$ is 40. What is $BE$?

正方形$ABCD$边长为10。点$E$在$\overline{BC}$上，$\triangle ABE$的面积为40。$BE$是多少？

(A) 4 4

(B) 5 5

(D) 7 7

(E) 8 8

Answer

Correct choice: (E)

正确答案：（E）

Solution

The legs of $\triangle ABE$ have lengths $AB = 10$ and $BE$. Therefore $\frac{1}{2} \cdot 10 \cdot BE = 40$, so $BE = 8$.

$\triangle ABE$的底为$AB = 10$，高为$BE$。因此$\frac{1}{2} \cdot 10 \cdot BE = 40$，所以$BE = 8$。

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