In a triangle, the lengths of the sides are 3,7,and 8. If the perimeter of a similar triangle is 54, what is the length of the longest side of the larger triangle?
*Im not sure on how to begin solving*
24
First triangle has a perimeter of 18 = 3 + 7 + 8.
54/18 = 3
So if they are "similar," each side must be three times larger.
84
To solve this problem, we can use the concept of similarity and ratios.
In a similar triangle, the ratio of the corresponding sides is equal. So, we can set up a proportion using the given information.
Let's represent the length of the longest side of the larger triangle as 'x'. Since we know the perimeter of the larger triangle is 54, we can set up the following proportion:
(3 + 7 + 8) / (x + 7 + 8) = 54 / x
Simplifying the left side of the equation:
18 / (x + 15) = 54 / x
To eliminate the fractions, we can cross-multiply:
18 * x = 54 * (x + 15)
18x = 54x + 810
54x - 18x = 810
36x = 810
Now, we can solve for 'x' by dividing both sides of the equation by 36:
x = 810 / 36
x = 22.5
Therefore, the length of the longest side of the larger triangle is 22.5 units.