Hello, webguy

I have a rectangle whose perimeter is 34 cm.

The diagonal is 13 cm, and the width is $\displaystyle x$ cm.

Derive the equation: $\displaystyle x^2-17x+60\:=\:0$ Code:

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| 13 * |
| * | x
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L

The length of the rectangle is $\displaystyle \,L.$

The width of the rectangle is $\displaystyle \,x$.

The perimeter is 34: .$\displaystyle 2L + 2x \:=\:34 \quad\Rightarrow\quad L \:=\:17 - x$ .[1]

Pythagorus says: .$\displaystyle x^2 + L^2 \:=\:13^2$

Substitute [1]: .$\displaystyle x^2 + (17-x)^2 \:=\:169$

. . . . . . . $\displaystyle x^2 + 289 - 34x + x^2 \:=\:169 $

. . . . . . . . . .$\displaystyle 2x^2 - 34x + 120 \;=\;0$

. . . . . . . . . . . $\displaystyle x^2 - 17x - 60 \:=\:0$