The diagram shows a triangle $XYZ$ in which $\angle XYZ=90{}^\circ $, \(XY=\left( 10-\sqrt{12} \

Question

The diagram shows a triangle $XYZ$ in which $\angle XYZ=90{}^\circ $, $XY=\left( 10-\sqrt{12} \right)\mathrm{ cm}$ and $YZ=\left( 2+\frac{1}{\sqrt{3}} \right)\mathrm{ cm}$ Find, the area of the triangle in the form $\left( a-\frac{b\sqrt{3}}{3} \right)$ cm$^{2}$ where $a$ and $b$ are integers, the value of ${{(XZ)}^{2}}$ in the form $\left( \frac{p-q\sqrt{3}}{3} \right)$ cm$^{2}$, where $p$ and $q$ are integers.

Accepted Answer

(a) $9-\frac{\sqrt3}{3}\text{ cm}^2$ (b) $\frac{349-116\sqrt3}{3}\text{ cm}^2$

Surds - Applications of Surds

Surds - Applications of Surds

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