The area of a right triangle is 15 cm^2 and the hypotneuse is 9 cm long. Find the lengths of the other two sides.

Expert Answers

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Let x and y be the two sides of the right triangle.

To solve, apply the formula of area of triangle.


So, plug-in b=x and h=y.



Then, isolate one of the variable.

`30/x =y`      (Let this be EQ1.)

Next, apply the Pythagorean formula.


Plug-in a=x and b=y and c=9.



Also, substitute EQ1.



Multiply both sides by x^2 to eliminate fraction in the equation.

`x^4 + 900 = 81x^2`

Then, set one side of the equation equal to zero.


To solve using quadratic formula, use another variable.

Let `z=x^2` .

`z^2 - 81z+900=0`

Then, plug-in a=1, b=-81 and c=900 to the quadratic formula.


`z=13.2925` and `67.7075`

Since `z=x^2` , then the values of x are:

`13.2925=x^2`          `67.7075=x^2`

`+-sqrt13.2925=x`        `+-sqrt67.7075=x`

`+-3.6459=x`              `+-8.2285=x`

However, consider only the positive values of x.

So, the values of x are:



Next, plug-in the values of x to EQ1.


`y=30/3.6459 =8.2284`


Hence, the length of the two sides of the right triangle are 3.6459 cm and 8.2284 cm.

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