Question

50 POINTS PLEASE HELP

Answer 1

Answer:

$perimeter= 5\sqrt{15} + 5\sqrt{5}$

Step-by-step explanation:

Given ,

A right angle triangle ΔABC with right angle at C and ∠A=30° and AC=5√5 units .

Let ∠A=A,∠B=B∠C=C and AC=b,BC=a,CA=b .

Implies perimeter of triangle = a+b+c .

now

$tanA=\frac{a}{b} \\\a=b*tanA\\a= 5\sqrt{5} *tan30^0\\a=\frac{5\sqrt{5}}{\sqrt{3}}$

and

$cosA=\frac{b}{c} \\\c=\frac{b}{cosA} \\c=\frac{10\sqrt{5}}{\sqrt{3} }$

implies ,

$perimeter = \frac{5\sqrt{5}}{\sqrt{3}} + 5\sqrt{5} +\frac{10\sqrt{5}}{\sqrt{3} }\\perimeter= 5\sqrt{15} + 5\sqrt{5}$

Answer 2

The third one down (c)