Find the value of X in the following rectangle if the area is 180 square inches

Mathematics

1 answer:

andrezito [222]2 years ago

7 0

Hello!

You find the area of a rectangle by the equation A = lw

A is area
l is length
w is width

Put in the values you know

180 = 3x * 6

Now you solve it algebraically

Divide both sides by 6

30 = 3x

Divide both sides by 3

10 = x

The answer is 10in

Hope this helps!

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Notice that the series can be written as a combination of two geometric series, that can be found independently:

$\frac{3^{n-1}-1}{6^{n-1}} =\frac{3^{n-1}}{6^{n-1}} -\frac{1}{6^{n-1}} =(\frac{1}{2})^{n-1} -\frac{1}{6^{n-1}}$

The first one: $(\frac{1}{2})^{n-1}$ is a geometric sequence of first term ( $a_1$ ) "1" and common ratio (r) " $\frac{1}{2}$ ", so since the common ratio is smaller than one, we can find an answer for the infinite addition of its terms, given by: $Infinite\,Sum=\frac{a_1}{1-r} = \frac{1}{1-\frac{1}{2} } =\frac{1}{\frac{1}{2} } =2$

The second one: $\frac{1}{6^{n-1}}$ is a geometric sequence of first term "1", and common ratio (r) " $\frac{1}{6}$ ". Again, since the common ratio is smaller than one, we can find its infinite sum: