Word problem using system of equations

[RHSLilSweetie07]

A right triangle has an area of 84 ft.^2 and a hypotenuse 25 ft. long. What are the lengths of its other two sides?

I know you have to solve a system of equations.

The equations I found were 1/2lw=84 and l^2+w^2=25.
Are these the right equations?

Could someone please help me solve this system of equations?

 

[stapel]

If you mean "(1/2)Lw = 84", then, yes, this is a useful equation. Solve it for one of the variables. Plug the result into the other equation, so you have the Pythagorean Theorem in terms of only one variable. Solve for the value(s) of that variable, and then back-solve for the value(s) of the other variable.

. . . . .(1/2)Lw = 84

. . . . .Lw = 168

. . . . .L = 168/w

. . . . .L² + w² = 25

. . . . .(168/w)² + w² = 25

...and so forth.

If you get stuck, please reply showing how far you have gotten. Thank you.

Eliz.

 

[RHSLilSweetie07]

I've done this much so far:

(168/w)^2 + w^2 =25
(28224/w^2) + w^2 = 25

This is where I get stuck. How can I get rid of the denominator (w^2)?

 

[tkhunny]

I've done this much so far:

(168/w)^2 + w^2 =25
(28224/w^2) + w^2 = 25

This is where I get stuck. How can I get rid of the denominator (w^2)?

You may first wish to note that it is 25², not just 25.

Hint: It is ONLY a quadratic equation. We're all pretty sure that w > 0, so multiply everything by w² and see if it looks more obvious.

Note: Way to go on the showing your work! Very helpful.

 

[stapel]

Multiply through by w².

Eliz.