the midpoints of each side of triangle NOT are connected to make a smaller triangle inside triangle NOT. If the area of triangle NOT is 16 in squared, what is the area of the smaller triangle?
Mrs.brown mr.green and mr.white live in houses that are brown green and white none of these people have a house or car that is the same color as there last name . mrs . brown has a car that is the same color as mr. white's house . what is the color of mr.greens house
To find the area of the smaller triangle inside triangle NOT, you can make use of the fact that the ratio of areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.
Let's label the midpoints of each side of triangle NOT as A', B', and C', and the smaller triangle as XYZ.
We know that the midpoints divide each side of the triangle into two equal lengths, so we can say that:
|NA'| = |A'T|
|OT| = |TB'|
|ON| = |NC'|
Since triangle NOT and triangle XYZ are similar triangles (by SAS similarity), the ratios of their corresponding side lengths are equal:
|A'X|/|OT| = |B'Y|/|NA'| = |C'Z|/|ON|
Let's represent the length of one side of triangle NOT as S. Then using the ratios above, we can represent the lengths of the corresponding sides of triangle XYZ as:
|A'X| = |B'Y| = |C'Z| = S/2
Now, we know that the area of triangle NOT is 16 in². Since triangle XYZ is similar to triangle NOT, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths:
area(XYZ)/area(NOT) = (|A'X|/|OT|)² = (S/2)/(S)² = 1/4
Therefore, the area of triangle XYZ is 16 in² multiplied by 1/4:
area(XYZ) = (16 in²) * (1/4) = 4 in²
So, the area of the smaller triangle inside triangle NOT is 4 in².