The ratio of the side length is 2:3:4. The shortest side is 15 inches. What is the perimeter? Explain.
The perimeter is 67.5 inches. If the first side is 15inches than the second side is 15+7.5= 22.5 because if you use a tape diagram the answer in each section is 7.5. Then that means your side 2 is 22.5 inches, then you do 22.5+7.5=30. Then just add them all together. You get a perimeter of 67.5 inches.
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Well, I must admit, this ratio has me feeling a bit "triangular." But fear not, for I have got just the trick up my sleeve!
Now, if the shortest side has a length of 15 inches, we can use this information to find the lengths of the other two sides. Since the ratio is given as 2:3:4, we can imagine that the shortest side corresponds to the 2 in the ratio.
To find the length of the medium side, we can set up a proportion:
2/15 = 3/x
Cross multiplying, we get:
2x = 45
Dividing both sides by 2 gives us:
x = 22.5
So, the length of the medium side is 22.5 inches.
To find the length of the longest side, we can set up a similar proportion:
2/15 = 4/y
Cross multiplying, we get:
4y = 60
Dividing both sides by 4 gives us:
y = 15
Surprisingly, the length of the longest side is 15 inches too!
Now, to find the perimeter, we simply add up the lengths of all three sides:
15 + 22.5 + 15 = 52.5
So, the perimeter of this triangle is 52.5 inches. And there you have it, my friend - we've successfully juggled our way through this geometry problem!
To find the perimeter of a triangle with ratio side lengths, we need to determine the actual lengths of the sides.
Given that the ratio of the side lengths is 2:3:4, we can set up a proportion using the shortest side length of 15 inches:
2/15 = 3/x = 4/y
To find the lengths of the other two sides, x and y, we can use cross multiplication:
2x = 15 * 3
x = (15 * 3) / 2
x = 22.5 inches
Similarly,
4y = 15 * 4
y = (15 * 4) / 4
y = 15 inches
Now that we have the lengths of all three sides, we can find the perimeter by adding them together:
Perimeter = 15 + 22.5 + 15
Perimeter = 52.5 inches
Therefore, the perimeter of the triangle with side lengths in the ratio 2:3:4 and the shortest side length of 15 inches is 52.5 inches.
let the sides be 2x, 3x, and 4x
(notice 2x:3x:4x = 2:3:4 )
but 2x = 15
find x, then sub into my definitions