Question

diego made a scale drawing of a football field. help you solve. scale width length area 1 yd = 1 yd 30 yd 60 yd 1,800 yd² 1 in = 3 yd 10 in 20 in 200 in² 1 in² =? yd² 200 × □ = 1,800 3³ 2² 3²⁰⁰ 3² 2³

Explanation:

Step1: Analyze the scale - factor relationship

The linear scale is 1 in = 3 yd. For area, the scale - factor relationship is based on the square of the linear scale - factor.

Step2: Calculate the conversion factor for area

If 1 in = 3 yd, then 1 in²=(3 yd)×(3 yd) = 9 yd². We know that the actual area is 1800 yd² and the scaled - down area is 200 in². Let the conversion factor from in² to yd² be \(x\). Then \(200x = 1800\), and \(x=\frac{1800}{200}=9\). Since the linear scale is 1 in = 3 yd, for area, the conversion is \(1\) in² \(=3^{2}\) yd².

Answer:

\(3^{2}\)