Question

In the given ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${90}^{\circ }$ triangle, side BC = 5 cm. Find length of side AC and side AB.


[3 Marks]

Answer 1

As the given triangle is ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${90}^{\circ }$ and the right angle is at vertex B, therefore, <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∠A = ∠C = ${45}^{\circ }$

As the given triangle is ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${45}^{\circ }$ - <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ${90}^{\circ }$ triangle, we know that each of the perpendicular sides is $\frac{1}{\sqrt{2}}$ of the hypotenuse. [1 Mark]

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> ∴ BC = $\frac{1}{\sqrt{2}}$ AC

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $\Rightarrow$ 5 = $\frac{1}{\sqrt{2}}$ AC

$\Rightarrow$ 5 $\times$ $\sqrt{2}$ = AC

∴ AC = 5$\sqrt{2}$ cm [1 Mark]

Similarly,
∴ AB = $\frac{1}{\sqrt{2}}$ AC

$\Rightarrow$ AB = $\frac{1}{\sqrt{2}}$ 5$\sqrt{2}$

$\Rightarrow$ AB = 5 cm [1 Mark]