- #1
Wilmer
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a^2 = k(k-u)(k-v)(k-w) where 2k = u+v+w
Given a, u and v, w = ?
Given a, u and v, w = ?
Wilmer said:a^2 = k(k-u)(k-v)(k-w) where 2k = u+v+w
Given a, u and v, w = ?
Wilmer said:I was able to get to:
w = SQRT[u^2 + v^2 + 2SQRT((uv)^2 - 4a^2)]
As you probably surmised, this is Heron's triangle area in disguise!
Example: triangle sides u,v,w: u=4, v=13, w=15 : a = area = 24
My solution will give correctly w = 15 using u=4:v=13 or u=13:v=4
But not if u=4, v=15: does not yield 13
Can you tell me why...thanks in advance...
The equation represents a quadratic relationship between the variable a and the variables k, u, v, and w. The value of k is determined by the sum of u, v, and w, which can provide insight into the relationship between the variables.
To solve the equation, you can use the quadratic formula or factor the equation into two binomials. Once the equation is in factored form, you can set each factor equal to zero and solve for the possible values of a, k, u, v, and w.
The equation can represent various real-life situations, such as the relationship between the area of a square (a^2) and the length of its side (k). The variables u, v, and w can represent different quantities that contribute to the overall length of the side.
One example is calculating the area of a trapezoid when given the length of the two parallel sides (u and v) and the length of the non-parallel sides (w). The equation can also be used to find the length of a side of a square when given the area and the value of k.
The equation is related to the concept of factoring and solving quadratic equations. It also involves the use of variables and their relationships to each other. In addition, the equation can be used in geometry to find the area or length of a shape.