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3 years ago

8

The length is 12 cm more than its width . Find the area of the rectangle if it's perimeter is 100 cm

1 answer:

DaniilM [7]3 years ago

6 0

Let's say the width is (x) and the width is (x+12). The formula for a perimeter of a rectangle equals 2w + 2l, which would then for this problem be 100=2(x) + 2(x+12) which would distribute as 2x + 2x + 12 which equals 4x+12. When you subtract twelve from 100 you get 88=4x. Divide 88 by 4 and you get x=22. This then would mean the width is 22 and the length is 34. The formula for an area of a rectangle is w*l. Plug in the numbers that you figure out from the area formula and you get 22x34=748

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Step-by-step explanation:

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3 0

3 years ago

Write the sum using summation notation, assuming the suggested pattern continues.

Usimov [2.4K]

Answer:

Sum of the sequence will be 648

Step-by-step explanation:

The given sequence is representing an arithmetic sequence.

Because every successive term of the sequence is having a common difference d = -3 - (-9) = -3 + 9 = 6

3 - (-3) = 3 + 3 = 6

Since last term of the sequence is 81

Therefore, by the explicit formula of an arithmetic sequence we can find the number of terms of this sequence

$T_{n}=a+(n-1)d$

where a = first term of the sequence

d = common difference

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Now we know sum of an arithmetic sequence is represented by

$\sum_{n=1}^{n}(a_{n})=\frac{n}{2}(a_{1}+a_{n})$

Now we have to find the sum of the given sequence

$S_{16}=\frac{16}{2}[-9 + (16-1)6]$

= 8[-9 + 90]

= 8×81

= 648

Therefore, sum of the terms of the given sequence will be 648.

6 0

3 years ago