A triangular flag has a height of 15 inches and a base length of 25 inches. Magnolia makes a scale drawing of the flag in which the base length is 10 inches. What is the area of Magnolia’s scale drawing? Solve the problem by computing the actual area from the scale drawing. Show your work. Make sure it isn't too long.
To find the area of Magnolia's scale drawing, we first need to determine the scale factor used. The scale factor is calculated by finding the ratio of the new base length to the original base length.
Scale factor = New base length / Original base length
Scale factor = 10 inches / 25 inches
Scale factor = 0.4
Next, we need to find the new height of the triangle in the scale drawing. We can do this by multiplying the original height by the scale factor.
New height = Original height * Scale factor
New height = 15 inches * 0.4
New height = 6 inches
Now that we have the height and base length of the triangle in the scale drawing, we can calculate the area using the formula for the area of a triangle:
Area = 0.5 * base * height
Area = 0.5 * 10 inches * 6 inches
Area = 30 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 30 square inches.
Too long
Apologies for that. Here is a shorter version:
1. Calculate the scale factor: 10 inches (new base length) / 25 inches (original base length) = 0.4
2. Determine the new height of the triangle in the scale drawing: 15 inches (original height) * 0.4 = 6 inches
3. Compute the area of the scale drawing using the formula for the area of a triangle: Area = 0.5 * 10 inches (base) * 6 inches (height) = 30 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 30 square inches.
All of it is AI generated
I apologize for the oversight. Let me provide you with a more concise answer:
1. Calculate the scale factor: 10 inches (new base length) / 25 inches (original base length) = 0.4
2. Determine the new height of the triangle in the scale drawing: 15 inches (original height) * 0.4 = 6 inches
3. Compute the area of the scale drawing using the formula for the area of a triangle: Area = 0.5 * 10 inches (base) * 6 inches (height) = 30 square inches
Therefore, the area of Magnolia's scale drawing of the flag is 30 square inches.
Make it different
Certainly! Here's another way to present the solution:
1. Find the scale factor: 10 inches (new base length) / 25 inches (original base length) = 0.4
2. Calculate the new height of the scaled triangle: 15 inches (original height) * 0.4 = 6 inches
3. Use the area formula for a triangle (Area = 0.5 * base * height) with the new dimensions: 0.5 * 10 inches * 6 inches = 30 square inches
Hence, the area of Magnolia's scale drawing of the flag is 30 square inches.