The sidesof a triangle are in the ratio 1/3:1/4:1/5 and its perimeter is 94 cm. The length of the smallest side is
24cm
24cm
24 cm.
To find the length of the smallest side of the triangle, we need to compare the ratios of the sides given.
Let's assume the ratio of the sides is 1/3 : 1/4 : 1/5. To simplify these fractions, we need to find their least common denominator (LCD), which is the smallest multiple of all the denominators. In this case, the LCD is 60.
Now, we can rewrite the ratios with a common denominator:
1/3 = 20/60
1/4 = 15/60
1/5 = 12/60
So, the ratio of the sides can be written as 20/60 : 15/60 : 12/60.
Next, we can assign variables to the sides of the triangle. Let's call the smallest side x. The other two sides would be (20/60)x and (15/60)x.
We know that the perimeter of the triangle is 94 cm. The perimeter is the sum of all three sides, so we can write the equation:
x + (20/60)x + (15/60)x = 94
To solve this equation, we need to combine like terms:
(1/1 + 20/60 + 15/60)x = 94
Simplifying the left side:
(60/60 + 20/60 + 15/60)x = 94
(95/60)x = 94
Now, we can solve for x by isolating it:
x = 94 / (95/60)
x = 94 * (60/95)
x ≈ 59.15
Therefore, the length of the smallest side of the triangle is approximately 59.15 cm.
change the ratios to more manageable numbers
1/3 : 1/4 : 1/5
= 20 : 15 : 12
= 20x : 15x : 12x
so 20x + 15x + 12x = 94
take over ...