The lengths of the sides of a triangle are in the extended ratio 3:10:12. The perimeter is 400 cm. What is the length of the longest side in centimeters?
Correct Answer is 192
can someone plz explain to me how it is 192
Let the common ratio be $x$, so the sides of the triangle are $3x$, $10x$, and $12x$. The perimeter is $3x + 10x + 12x = 25x$, so $25x = 400$ and $x = 16$. Therefore, the longest side is $12x = 12(16) = \boxed{192}$ cm.
i still dont understand
When we see "extended ratio", this means that the actual lengths of the sides are in the ratio $(3x):(10x):(12x)$ for some number $x$.
The perimeter of the triangle is the sum of the lengths of its sides, which is $$3x+10x+12x=25x.$$ We are given that the perimeter is 400 cm, so we can set up the equation $$25x=400.$$ Solving for $x$, we find that $x=16$.
Therefore, the length of the longest side is $12x=12\cdot 16 = \boxed{192}$ cm.
To find the length of the longest side of the triangle, we need to determine the actual lengths of the sides using the given extended ratio.
Let's assume the common ratio is 'x'. So, the lengths of the sides are 3x, 10x, and 12x.
We are also given that the perimeter of the triangle is 400 cm. The perimeter of a triangle is the sum of the lengths of all its sides. So, we can write the equation:
3x + 10x + 12x = 400
Simplifying the equation, we have:
25x = 400
Dividing both sides of the equation by 25, we get:
x = 400 / 25 = 16
Now that we know the value of 'x', we can substitute it back into the lengths of the sides:
Longest side = 12x = 12 * 16 = 192 cm
So, the length of the longest side of the triangle is 192 cm.