If the sides of a triangle measure 8,9,and 10 find the longest side of a similar triangle whose perimeter is 81.
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The perimeter of the triangle whose dimensions we know is 27. Therefore, the proportion of each side of the two triangles must be 81:27 which happens to be 3:1.
To find the longest side of the second triangle, we set up the following equation:
3/1 = x/10
Now we cross multiply to find for x.
x = 30
This makes sense because the second triangle is 3 times the size of the first so each side of the second triangle must be 3 times the length of the corresponding side on the first triangle.
So, the longest side of the second triangle is 30 units long.
First,we'll calculate the perimeter of the original triangle, adding up the three lengths of the sides:
P1 = 8+9+10
P1 = 27
Now, we'll divide the perimeter of the similar triangle, namely 81, by the perimeter of the original triangle:
P2 = 81
P2/P1 = 81/27
P2/P1 = 3 units
So, the rapport is of 3 units. We'll multiply the length of each side of the original triangle by 3:
8*3 = 24 units
9*3 = 27 units
10*3 = 30 units
The longest length of the side of the similar triangle is of 30 units.
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