To find the ratio of the areas of the two triangles, we can use the formula for the area of a triangle:
Area = 1/2 * base * height
For the smaller triangle:
Base = 5 - 2 = 3
Height = 9 - 3 = 6
Area = 1/2 * 3 * 6 = 9
For the larger triangle:
Base = 12 - 10 = 2
Height = 6 - 2 = 4
Area = 1/2 * 2 * 4 = 4
Therefore, the ratio of the area of the smaller triangle to the area of the larger triangle is 9:4.
Use the image to answer the question.
An illustration shows the first quadrant of a coordinate plane. The x-axis and the y-axis range from 0 to 15. Two right triangles are graphed on the plane. One triangle is formed by connecting points plotted at coordinates left parenthesis 5 comma 9 right parenthesis, left parenthesis 5 comma 3 right parenthesis, and left parenthesis 2 comma 3 right parenthesis. The sides of this triangle are formed by solid lines. The second triangle is formed by connecting points plotted at coordinates left parenthesis 12 comma 6 right parenthesis, left parenthesis 12 comma 2 right parenthesis, and left parenthesis 10 comma 2 right parenthesis. The sides of this triangle are formed by dotted lines.
What is the ratio of the area of the smaller triangle in relation to the area of the larger triangle?
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