Question

Find the perimeter of the following isosceles triangle. show work

Answer 1

Answer

Find out the perimeter of the isosceles triangle.

To prove

As shown in the figure.

P(0,4) , Q(-2,0) and R(2,0) are the vertices of the triangle PQR.

Formula

$Distance\ formula = \sqrt{(x_{2} - x_{1})^{2} +(y_{2} -y_{1})^{2}}$

As P(0,4) and Q(-2,0)

$PQ = \sqrt{(-2 - 0)^{2} +(0 - 4)^{2}}$

$PQ = \sqrt{4+16}$  

$PQ = \sqrt{20}\unit$

In the isoceles triangle the two sides of the triangles are equal .

Therefore PQ = PR

$PR = \sqrt{20}\unit$

As Q(-2,0) and R(2,0)

$QR = \sqrt{(2- (-2))^{2} +(0 - 0)^{2}}$

$QR = \sqrt{(4)^{2}}$

QR = 16 unit

$Perimeter\ of\ triangle PQR = \sqrt{20} +\sqrt{20} + 16$

$Perimeter\ of\ triangle PQR = 4\sqrt{5} + 16\ units^{2}$