Question

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

Answer 1

i still dont understand

Answer 2

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.

Answer 3

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.