1cm = 6in
1cm = 2in
Above are two different models of the same triangular handkerchief. If the area of the model on the right is 108 sq cm, what is the area of the model on the left?
First, we need to compare the two different models based on the given conversion rates:
1cm = 6in
1cm = 2in
To compare the areas, we need to look at the relationship between the sides of the two models.
Let's assume the base of the triangle on the left model is x cm. Using the conversion rate of 1cm = 2in, the base of the triangle on the left model in inches would be 2x inches.
Similarly, let's assume the height of the triangle on the left model is y cm. Using the conversion rate of 1cm = 2in, the height of the triangle on the left model in inches would be 2y inches.
Therefore, the area of the model on the left would be:
Area_left = (1/2) * base_left * height_left
Area_left = (1/2) * 2x * 2y
Area_left = 2xy
Now, let's find the relationship between the areas of the two models:
Area_right = 108 sq cm
Area_left = 2xy
We know that the conversion rate between the two models is:
1cm = 6in
Therefore, the relationship between the areas can be expressed as:
Area_left = (6/1)^2 * Area_right
Area_left = 36 * 108
Area_left = 3888 sq in
So, the area of the model on the left is 3888 sq in.