Step-by-step answer:
Given: a picture frame is twice as wide as it is high and has an area of 4050 cm^2. Find its dimensions.
Method 1: solve mentally
A quick mental way to solve the problem is to imagine cutting into two lengthwise. Each half will be a square of 4050/2=2025 cm^2 = 45cm *45 cm
Therefore the frame is 45cm * 90 cm.
Method 2: Using Algebra if pencil and paper is available
Let H=height of the frame
Then 2H = Length of the frame.
Area of frame = Length * Height = 2H *H =4050 cm^2
Solve for H :
2H^2 = 4050
H^2 = 4050/2 = 2025
H = sqrt(2025) = 45 cm
Length = 2H = 90 cm
