Question

si un cuadrado de 9 dm de lado y un triángulo equilatero tienen el mismo perímetro ¿cuál es la medida del lado del triángulo?​

Answer 1

Respuesta:

12dm

Explicación paso a paso:

Let's solve for the perimeter of the square using the formula P=4s, where s is the length of its sides.

$\large \begin{aligned} &\sf P=4s \\&\sf P=4 \times 9dm \\&\sf P=36dm\end{aligned}$

Now, let's solve for the sides of the triangle.

$\large \begin{aligned} \sf P&=\sf 3s \\\sf 36dm&=\sf 3s \\\sf \frac{36dm}{3}&=\sf s \\\sf s&=\sf\frac{36dm}{3} \\\sf s&=\boxed{\color{blue}{\sf 12dm}} \end{aligned}$

Therefore, the sides of the triangle measures 12dm.

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If you want a shorter solution, here it is.

$\large \begin{array}{|c|}\hline \begin{aligned}&\textsf{Let x be the sides of the square.} \\&\textsf{Let y be the sides of the triangle.} \end{aligned} \\ \begin{aligned}\sf P_{\square}&=\sf P_{\triangle}\\\sf 4x&=\sf 3y\\\sf 4 \times 9dm&=\sf 3y\\\sf 36dm&=\sf 3y\\\sf \frac{36dm}{3}&=\sf y\\\sf \boxed{\color{blue}{\sf 12dm}}&=\ \color{black}{\textsf{sides of the triangle}}\end{aligned}\\\hline \end{array}$