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# Geometry Question

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If AC = 36 inches, what is the measure of AB. (Please See Attached)

Jul 8, 2020

#1
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If $$AC = 36$$ inches, what is the measure of AB. (Please See Attached)

$$\begin{array}{|rcll|} \hline \mathbf{(2x-6) + (x^2-13x)} &=& \mathbf{36} \\ x^2-11x-6 &=& 36 \\ \mathbf{x^2-11x-42} &=& \mathbf{0} \\\\ x &=& \dfrac{11\pm \sqrt{11^2-4*(-42)} } {2} \\\\ x &=& \dfrac{11\pm \sqrt{121+168} } {2} \\\\ x &=& \dfrac{11\pm \sqrt{289} } {2} \\\\ x &=& \dfrac{11\pm 17 } {2} \\\\ x &=& \dfrac{11 \mathbf{+} 17 } {2} \quad | \quad x > 0! \\\\ \mathbf{x} &=& \mathbf{14} \\\\ \mathbf{\text{AB}} &=& \mathbf{2x-6} \\ \text{AB} &=& 2*14-6 \\ \mathbf{\text{AB}} &=& \mathbf{22\ \text{inches}} \\ \hline \end{array}$$

Jul 9, 2020