the perimeter of a angle is 40 inches the ratio of lengths is 3:4:6: find the shortest side lengths
the perimeter of a angle is 40 inches the ratio of lengths is 3:4:6: find the shortest side lengths
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The perimeter of a triangle is 40 inches the ratio of lengths is 3:4:6: find the shortest side lengths.
then:
You make the sides of the triangle 3 x, 4 x, and 6 x, where x is the scaling factor that will bring the total up to 40 in.
Perimeter:
P = 3 x + 4 x + 6 x
40 = 13 x
Divide both sides by 13
40 / 13 = x
x = 40 / 13
Your shortest side is the 3 x, so its length = 3 ∙ 40 / 13 = 120 / 13 in
Approx. 3 x = 9.23 in
To find the shortest side lengths, we need to determine the values of the lengths in the ratio 3:4:6.
Let's assume the lengths of the sides are 3x, 4x, and 6x (where x is a common factor for all three lengths).
Given that the perimeter of the triangle is 40 inches, we can write the equation:
3x + 4x + 6x = 40
Combine like terms:
13x = 40
To solve for x, divide both sides of the equation by 13:
x = 40/13
Now, we can substitute the value of x back into the lengths of the sides:
Shortest side length = 3x = 3 * (40/13) = 120/13 inches
Therefore, the shortest side length is 120/13 inches.