jpr200012 wrote:

Area of frame + picture = 65

Since both have the same area, 65/2 = 32.5 - each are is 32.5.

The picture is a similar triangle to larger triangle. Therefore, the angles are the same and the sides are proportional.

Height must be less than 10. Base must be less than 13.

Area of picture = 1/2 b h = 32.5. bh = 65.

What two numbers add to 17 and multiply to 65, and are in proportion to h = 10, b = 13, and hypotenuse \(sqrt(269)\)?

I'm stuck on how to proceed. I can at least eliminate C, D, E.

You almost nailed it ...! Let me complete the rest for you.

Lets assume the sides of the picture as \(X\) and \(Y\) and Hypotenuse as \(Z\)

Then we have \(X + Y = 17 -- > 1\)

and \(X*Y = 65 -- >2\)

We need \(\sqrt{X^2 + Y ^2} = Z\)

Square both the sides of equation \(1\)

\((X + Y)^2 = 17^2 = 289\)

\(X^2 + Y^2 + 2*X*Y = 289\)

\(X^2 + Y^2 + 2 *65 = 289\)

\(X^2 + Y^2 = 159 -- > 3\)

Take the square root of equation \(3\)

\(\sqrt{X^2 + Y ^2} = \sqrt{159}= Z\)

Hence B.

Hope it helps.