Question

$\huge \tt \color{aqua} \star \:Question \: \star$

The hypotenuse of a Right triangle is 4√5cm.if the smaller side is tripled and the larger side is doubled , the new hypotenuse will be 20cm .find the length of each side.

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Answer 1

$\red{\bf {Answer:}}$

$\sf{4, 8, 4√5}$

$\red{\bf {Step-by-step\: explanation}}$

We can use the Pythagorean Theorem for this

$\begin{gathered}a^2+b^2 = (4\sqrt{5})^2\\=a^2+b^2 = 80\end{gathered}$

$\red{\bf {We\: can\: also\: write}}$

$\begin{gathered}(3a)^2+(2b)^2=20^2\\= 9a^2+4b^2 = 400\end{gathered}$

We can multiply the first equation by 4 to get

$\sf{4a^2+4b^2=320}$

Subtracting the first equation from the second we get

$\begin{gathered}5a^2=80\\a^2 = 16\\a=4\end{gathered}$

$\red{\bf {Solving\: for \:b\: we\: get}}$

$\color{purple}\underline{\underline{ \tt{{ \boxed {b = 8} }}}}$

$\small\textbf\color{teal}{Thus our sides are 4, 8, 4√5}$

Thankyou :)