AMC10 2003 B

AMC10 2003 B · Q6

AMC10 2003 B · Q6. It mainly tests Pythagorean theorem, Ratios in geometry.

Many television screens are rectangles that are measured by the length of their diagonals. The ratio of the horizontal length to the height in a standard television screen is 4 : 3. The horizontal length of a “27-inch” television screen is closest, in inches, to which of the following? [Diagram shows a rectangle labeled “Length” (horizontal), “Height” (vertical), and “Diagonal”]

许多电视屏幕是长宽比为 4 : 3 的矩形，以对角线长度来测量尺寸。“27英寸”电视屏幕的水平长度（英寸）最接近于下列哪个选项？[图示一个矩形，标有“Length”（水平）、“Height”（垂直）和“Diagonal”]

(A) 20 20

(B) 20.5 20.5

(D) 21.5 21.5

(E) 22 22

Answer

Correct choice: (D)

正确答案：（D）

Solution

(D) The height, length, and diagonal are in the ratio $3:4:5$. The length of the diagonal is $27$, so the horizontal length is $\frac{4}{5}(27)=21.6$ inches.

（D）高度、长度和对角线的比为 $3:4:5$。对角线长度为 $27$，因此水平长度为 $\frac{4}{5}(27)=21.6$ 英寸。

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