The ratio of a triangle's sides is 4:3:6. If the length of the hypotenuse is 1/4, what is the value of the length of the short leg of the triangle subtracted from the length of the long leg of the triangle? Help please?
since 1/4 = 6/24, use that ratio for all the numbers. Then you have
1/6 : 1/8 : 1/4
1/6 - 1/8 = 1/24
Or, 4-3 = 1
Now scale that and you get 1/24
To solve this problem, we need to find the lengths of the triangle's sides first. Let's denote the shortest side as a, the middle side as b, and the longest side as c.
Given that the ratio of the sides is 4:3:6, we can express the lengths of the sides as:
a = 4x
b = 3x
c = 6x
To find the value of x, we can use the fact that the length of the hypotenuse is equal to 1/4. The hypotenuse is the longest side, so we have:
c = 1/4
Substituting the expression for c, we can solve for x:
6x = 1/4
x = (1/4) / 6
x = 1/24
Now that we know the value of x, we can find the lengths of the sides:
a = 4x = 4 * (1/24) = 1/6
b = 3x = 3 * (1/24) = 1/8
c = 6x = 6 * (1/24) = 1/4
Finally, we need to calculate the value of the length of the long leg minus the length of the short leg:
Long leg - Short leg = (1/4) - (1/6) = (3/12) - (2/12) = 1/12
Therefore, the value of the length of the short leg of the triangle subtracted from the length of the long leg is 1/12.