The sides of a triangle are in the ratio 6:8:10. The perimeter is 120 cm. Find the length of the shortest side.
6 + 8 + 10 = 24 ... 24 r = 120 ... r = 5 ... 6 r = 30
let the sides be 6x, 8x, and 10x
then 6x+8x+10x = 120
x = 5
The shortest side is 6x = 6(5) = 30
(in effect that is what R_scott did)
btw, did you notice that the triangle is right-angled ?
6 x + 8 x + 10 x = 120
24 x = 120
x = 120 / 24 = 5
Shortest side = 6 x = 6 ∙ 5 = 30 cm
To find the length of the shortest side of the triangle, we need to determine the corresponding ratio for each side. From the given information, the ratio of the sides is 6:8:10.
To determine the actual lengths of the sides, we can assign a common multiple to the ratio. Let's assume the common multiple is x, so the sides of the triangle become:
Shortest side: 6x
Second side: 8x
Longest side: 10x
The perimeter of a triangle is the sum of its three sides. In this case, the perimeter is given as 120 cm. Therefore, we can set up the equation:
6x + 8x + 10x = 120
Now, let's solve for x:
24x = 120
x = 120 / 24
x = 5
Now that we have the value of x, we can substitute it back into the ratio to find the lengths of the sides:
Shortest side = 6 * x = 6 * 5 = 30 cm
Therefore, the length of the shortest side of the triangle is 30 cm.