SOLUTION: Hello, I'm not sure how to figure this out so that i may explain it to my daughter. The question is below. i'm thinking since the area is 1/2 it would be 15 and 11. A secon

Question 698005: Hello, I'm not sure how to figure this out so that i may explain it to my daughter. The question is below. i'm thinking since the area is 1/2 it would be 15 and 11.
A second triangle is similar to and has dimensions that are half as long as the triangle on the left. Find the area of this larger triangle (drawn to the left) and the area of the second triangle. draw the smaller triangle and label the correct dimension. area of a triangle 1/2 bh.
outside 30 in
inside 22 in

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If this was homework, it is probably too late for the solution to help the grade, but the explanation may help the understanding.
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Your posted question did not show a drawing, but I imagine your problem looked like this:
The length of the horizontal, bottom side of the triangle is called the base, represented by b.
The height of the triangle, represented by h, and for the large triangle, it is the length of the vertical green line.
If I imagined the drawing correctly, b=30 inches and h=22 inches.
The area of the large triangle (in square inches) can be calculated as half of the product of base times height:
so which calculates as square inches.

The smaller triangle is similar, which in geometry means a scaled down or scaled up version with the same shape.
All the dimensions are half as long as the triangle on the left,
so you are correct that the corresponding dimnsions are inches and inches.
In my drawing, I would show that as:

The area of the smaller triangle would be calculated as
, in this case which calculates as square inches.
Notice that as the smaller triangle was made half as wide and half as tall, its area ended up being 1/4 (half of half) of the area of the large triangle.
As you multiply dimensions, the scaling factors multiply too.
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