Question

Find the sides of the triangle if two of it's sides are equal, the third side is 1 1/3 cm longer than the others and it's prerimeter is 2 2/5 cm.

Answer 1

let's firstly convert the mixed fractions to improper fractions and then sum them up.

`\stackrel{mixed}{1(1)/(3)}\implies \cfrac{1\cdot 3+1}{3}\implies \stackrel{improper}{\cfrac{4}{3}} ~\hfill \stackrel{mixed}{2(2)/(5)} \implies \cfrac{2\cdot 5+2}{5} \implies \stackrel{improper}{\cfrac{12}{5}} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{equal sides}}{x+x}~~ + ~~\stackrel{\textit{third side}}{\left( x+\cfrac{4}{3} \right)} ~~ = ~~\stackrel{perimeter}{\cfrac{12}{5}}\implies 3x+\cfrac{4}{3}=\cfrac{12}{5}`

`\stackrel{\textit{multiplying both sides by }\stackrel{LCD}{15}}{15\left( 3x+\cfrac{4}{3} \right)=15\left( \cfrac{12}{5} \right)}\implies 45x+20=36\implies 45x=16 \\\\\\ \stackrel{\textit{equal sides}}{\boxed{x=\cfrac{16}{45}}}\hspace{10em}x+\cfrac{4}{3}\implies \cfrac{16}{45}+\cfrac{4}{3}\implies \stackrel{\textit{third side}}{\boxed{\cfrac{76}{45}}}`