SOLUTION: The area of a right triangle is 105m^2. The hypotenuse has length square root 421m. What are the lengths of the legs?
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Question 1039482: The area of a right triangle is 105m^2. The hypotenuse has length square root 421m. What are the lengths of the legs? Found 3 solutions by stanbon, Aldorozos, MathTherapy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! The area of a right triangle is 105m^2. The hypotenuse has length square root 421m. What are the lengths of the legs?
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Equations:
L*W = 105
L^2 + W^2 = 421
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Substitute for "L" and solve for "W":
L = 105/W
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(105/W)^2 + W^2 = 421
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105 + W^4 = 421 W^2
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W^4 - 421W^2 + 105 = 0
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Ans: Width = 20.51
Length = 421/20.51 = 20.53
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Cheers,
Stan H.
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You can put this solution on YOUR website! Let's assume one side as x and the other side as y. We have to find the values of x and y
We have two equations and two unknowns.
The first equation is x*y *1/2 = 105m^2 = area
The second equation is from Pythagorean theorem
x^2 + y^2 = (Sqrt 421m)^2 = 421m
Now we have both equations
x*y *1/2 = 105m^2
x^2 + y^2 = 421m
We can calculate the value of y from the first equation in terms of x and replace the y of the second equation with what we found for x from the first equation.
x*y *1/2 = 105m^2 therefore x*y = 2(105m^2) and then y = 210m^2/x now we can replace y in the second equation with 210m^2/x
x^2 + (210m^2/x)^2 = (421m)^2
x^2 + (210m^2)^2/x^2 = (421m)^2
Lets multiply both sides of the equation by x^2 to get rid of x^2 in the denomination
x^4 + (210m^2)^2 = (421m)^2 *x^2
x^4 - (421m)^2 *x^2 + (210m^2)^2 = 0
This is similar to a quadratic equation Lets assume x^2 = z Then we can rewrite the equation
z^2 - (421m)^2 *z + (210m^2)^2 = 0 This is a quadratic equation If we solve this quadratic equation we find z in terms of m. For example z = 9m^2 (please note 9m^2 is a hypothetical example. To get the accurate number we have to solve the quadratic equation
If z = 9m^2 then x^2 = 9m^2 and therefore x = 3m Now that we found x we can use one of the equations to find y.
The easiest is to use x.y/2 = 105m^2 we know x = 3m Therefore 3m.y/2 = 105m^2
and this allows us to calculate y in terms of m. We have to multiply both sides by two and then divide both sides by three. To calculate the exact values of x and y of course we have to solve the quadratic equation:
z^2 - (421m)^2 *z + (210m^2)^2 = 0
You can put this solution on YOUR website! The area of a right triangle is 105m^2. The hypotenuse has length square root 421m. What are the lengths of the legs?
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