# The length of the hypotenuse of a right isosceles triangle is 4√3 What is the perimeter of the triangle?

Jun 14, 2015

Permeter$= 16.7$

#### Explanation:

Try this:

Jun 15, 2015

The perimeter of the triangle is " "$\textcolor{b l u e}{16.72616}$ units.

#### Explanation:

Perimeter=AB+BC+CA

$P = A B + A C + 4 \sqrt{3}$ [since AC=hypotenuse]

$P = A C + A C + 4 \sqrt{3}$[since it is a isosceles triangle]

$p = 2 A C + 4 \sqrt{3}$ $\text{ } \textcolor{b l u e}{\left(1\right)}$

$\sin \theta$=opposite side/hypotenuse

$\sin {45}^{\circ} = \frac{A C}{C B}$

$A C = \left(B C\right) \times \sin {45}^{\circ}$

$A C = \left(B C\right) \times \frac{1}{\sqrt{2}}$[from angle table]

$A C = \left(4 \sqrt{3} \times \frac{1}{\sqrt{2}}\right)$

$A C = \frac{4 \sqrt{3}}{\sqrt{2}}$

substitute the above value in $\text{ } \textcolor{b l u e}{\left(1\right)}$

$P = \left(2 \times \frac{4 \sqrt{3}}{\sqrt{2}}\right) + \left(4 \sqrt{3}\right)$

$P = \left(\frac{8 \sqrt{3}}{\sqrt{2}}\right) + 4 \sqrt{3}$

$P =$ $\textcolor{b l u e}{16.72616}$ units.