Question

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

Answer 1

\[\frac{1}{2}bh=84\]
\[b^2+h^2=25^2\]

Answer 2

Solve the system

Answer 3

That's where I'm stuck at

Answer 4

Solve the first equation for b and replace b in the second equation with that expression.

Answer 5

I got 168/h^2+h^2=25^2

Answer 6

Why is it 168/h^2?

Answer 7

Because bh/2=84 so to get rid of the 2 I multiply 2 on both side and you get bh=168. To get b alone you divide h and both side then you said to plug it in

Answer 8

So if you divide both sides by h, how do you get 168/h^2?

Answer 9

Plug it in to b^2+h^2=25^2

Answer 10

My point is that b = 168/h

Answer 11

So, yes, plug it in.

Answer 12

\[(\frac{168}{h})^2+h^2=625\]

Answer 13

Okay then what?

Answer 14

Square 168/h

Answer 15

Okay then..

Answer 16

1. Multiply both sides by h^2
2. Set the equation equal to 0
3. Factor if possible
4. If it won't factor, plug it into the quadratic formula.