How does tripling the side lengths of a right triangle affect its area?)

Mathematics

2 answers:

Furkat [3]2 years ago

7 0

Answer:

The area would increase 6 times

Explanation:

The area of the triangle can be calculated as follows:

area = $\frac{1}{2} * base * height$

Tripling the side lengths of a right triangle would mean that:

new base = 3 * base

new height = 3 * height

Substitute with the new values in the equation:

new area = $\frac{1}{2} * 3 * base * 3 * height$

new area = $6 (\frac{1}{2} * base * height)$

Comparing the new area with the original one, we can conclude that by tripling the side lengths of the right triangle, the area of the triangle will increase 6 times.

Hope this helps :)

kap26 [50]2 years ago

6 0

The area of the triangle will then be 9 times as great.

The formula of the area of a triangle is 1/2bh, so if the base has been tripled and the height has been tripled, you're essentially multiplying 3 to the original equation twice (3 x 3 = 9).

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Neko [114]

Answer:

Step-by-step explanation:

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5 0

2 years ago

likoan [24]

It's easy to show that $7\tan(4x)$ is strictly increasing on $x\in\left[0,\frac\pi8\right]$ . This means

$M = \max \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/12} = 7\sqrt3$

and

$m = \min \left\{7\tan(4x) \mid \dfrac\pi{16} \le x \le \dfrac\pi{12}\right\} = 7\tan(4x) \bigg|_{x=\pi/16} = 7$

Then the integral is bounded by

$\displaystyle 7\left(\frac\pi{12} - \frac\pi{16}\right) \le \int_{\pi/16}^{\pi/12} 7\tan(4x) \, dx \le 7\sqrt3 \left(\frac\pi{12} - \frac\pi{16}\right)$