Area and Perimeter Practice Test 2

Suppose, the three sides of the triangle are a, b and c and a is the largest while c is the smallest side of the triangle.
Now, (a + b + c) = c × 6
⇒ a + b = 5c
Again, ${\mathit{a}}^2\mathit{–}{\mathit{b}}^2$ = ${\mathit{c}}^2$
⇒ (a + b) (a – b) = ${\mathit{c}}^2$
⇒ 5c (a – b) = ${\mathit{c}}^2$
⇒ a - b = $\frac{\mathit{c}}{5}$ [Since a + b = 5c]
Now, a + b = 5c, a – b = $\frac{\mathit{c}}{5}$
Since, a = $\frac{1}{2}\left(5\mathit{c}+\frac{\mathit{c}}{5}\right)$ = $\frac{13\mathit{c}}{5}$ and b = $\frac{1}{2}\left(5\mathit{c}-\frac{\mathit{c}}{5}\right)$ = $\frac{12\mathit{c}}{5}$
Hence, a : b : c = $\frac{13\mathit{c}}{5}:\frac{12\mathit{c}}{5}:\mathit{c}$ = 13 : 12 : 5