the lengths of the sides of a triangle are in the radio 5 : 6 : 7. if the perimeter is less than 54 cm , what is the length of the longest side?
5 + 6 + 7 = 18 ... 54 / 18 = ?
multiply the result by the largest number in the ratio
To find the length of the longest side, we need to determine the ratios given and use them to calculate the actual lengths of the sides.
Let's assume that the common ratio for the three sides is represented by "x". In this case, the three sides can be expressed as 5x, 6x, and 7x.
Since the perimeter is the sum of all three sides, we can write the equation:
5x + 6x + 7x < 54
Combining like terms, we have:
18x < 54
Now we solve for x:
x < 54/18
x < 3
Since we want to find the length of the longest side, which is represented by 7x, we substitute x = 3 into the equation:
7(3) = 21
The length of the longest side is 21 cm.