Question

in a scale drawing of a painting, 1 centimeter represents 10 inches. scale 1 cm : 10 in answer the following. (a) the height of the real painting is? inches. what is the height of the painting in the scale drawing? centimeters (b) in the scale drawing, the length of the painting is 9 centimeters. what is the length of the real painting? inches

Explanation:

Part (a)

Step1: Identify the scale

The scale is \( 1 \, \text{cm} : 10 \, \text{in} \), meaning \( 1 \) centimeter in the drawing represents \( 10 \) inches in real. Let the real height be \( h_{real} \) and the drawing height be \( h_{drawing} \). We know \( h_{real} = 90 \) inches (assuming the missing number is 90, as the arrow might be covering it, but let's proceed with the logic). The formula is \( h_{drawing}=\frac{h_{real}}{10} \) (since \( 1 \, \text{cm} = 10 \, \text{in} \), so inches to cm: divide by 10).

Step2: Calculate drawing height

If \( h_{real} = 90 \) inches, then \( h_{drawing}=\frac{90}{10}=9 \) centimeters. Wait, but maybe the real height is 90? Wait, the original problem's (a) has a missing number, but looking at (b), maybe (a) real height is 90? Wait, no, let's check the problem again. Wait, the user's image: (a) "The height of the real painting is [missing] inches. What is the height of the painting in the scale drawing?" Wait, maybe the missing number is 90? Or maybe it's a typo. Wait, but in (b), the drawing length is 9 cm, real length is 9*10=90 inches. So maybe (a) real height is 90 inches? Let's assume that. So step1: scale is 1 cm = 10 in. Step2: to find drawing height, divide real height by 10. So if real height is 90 inches, drawing height is 90/10=9 cm.

Part (b)

Step1: Identify the scale

Scale is \( 1 \, \text{cm} : 10 \, \text{in} \), so drawing length \( l_{drawing} \) to real length \( l_{real} \) is \( l_{real}=l_{drawing} \times 10 \).

Step2: Calculate real length

Given \( l_{drawing} = 9 \) cm, so \( l_{real}=9 \times 10 = 90 \) inches.

Answer:

s:
(a) \(\boldsymbol{9}\) (assuming real height is 90 inches, as per (b)'s context)
(b) \(\boldsymbol{90}\)