Question

A triangle has an area of 30 cm2. The base and height are scaled by a factor of 3. What is the are of the resulting triangle.

Answer 1

The base and height scaled to some factor, simply means,
they're blown up by that much, or multiplied by that much,

in this case is 3, so.. the area would be 1/2 bh, now,
with 3b and 3h, what would it be?

$\bf \begin{cases} A=\cfrac{1}{2}bh \\\\ \textit{now, scaling "b" and "h" by 3} \\\\ A=\cfrac{1}{2}\cdot 3b\cdot 3h\to \cfrac{1}{2}\cdot 9bh \\\\ A=\cfrac{9}{2}bh\to 9\left(\cfrac{1}{2}bh \right)\\ --------------\\ 9\left(\cfrac{1}{2}bh \right)\textit{ is really 9 times }\cfrac{1}{2}bh \\\\ \textit{whatever the value of }\cfrac{1}{2}bh \textit{may be} \end{cases}$

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$\bf A=\cfrac{1}{2}bh\qquad \begin{cases} b=2\\ h=3 \end{cases}\implies A=\cfrac{1}{2}\cdot 2\cdot 3\to 3 \\\\\\ \textit{now, let us scale "b" and "h" by 3} \\\\ A=\cfrac{1}{2}\cdot 3b\cdot 3h\qquad \begin{cases} b=2\\ h=3 \end{cases}\implies A=\cfrac{1}{2}\cdot (3\cdot 2)\cdot (3\cdot 3) \\\\\\ A=\cfrac{1}{2}\cdot 6\cdot 9\to 3\cdot 9\to 27$