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tankabanditka [31]
2 years ago
13

A rectangle has a perimeter of 46 meters and a base of 8 meters. What is the height?​

Mathematics
1 answer:
Igoryamba2 years ago
3 0

Answer:

15 metres

Step-by-step explanation:

perimeter of rectangle = 2(base + height)

=2(8+h) = 46

= 16 + 2h = 46

= 2h = 46 - 16

= 2h = 30

= h = 15

15 metres is the height of rectangle

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Use your creativity... Write a short story/problem/question that can be described by the scenario of 4 divided by 1/2
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Solve the following system of equations express your answers as an ordered pair in the format (a,b) with no spaces between the n
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Read 2 more answers
The first three terms of an arithmetic progression are m,12 and n . Find the value of m+n​
Vera_Pavlovna [14]
<h3>Answer:  24</h3>

===========================================

Explanation:

There are a few approaches. Here's one way to solve.

Let d be the common difference between the terms.

We add d to each term of this arithmetic sequence to get the next term.

  • First term = m
  • Second term = 12 = m+d
  • Third term = n = (m+d)+d = m+2d

Focusing on the second equation, we can solve for d like so

m+d = 12

d = 12-m

This is then plugged into the third equation

n = m+2d

n = m+2(12-m)

n = m+24-2m

n = 24-m

Therefore,

m+n = m+(24-m) = 24

It turns out that it doesn't matter what m and n are because m+n is always equal to 24 in this case.

-----------------

A more concrete example:

Let's say m = 2. We won't set up n just yet but we'll be able to compute it fairly soon.

Since m = 2, this means d = 12-m = 12-2 = 10. This is the gap between adjacent or neighboring terms.

If d = 10, then the third term must be n = 12+d = 12+10 = 22

We can then see that m+n = 2+22 = 24

-----------------

I'll do another example:

m = 5

d = 12-m = 12-5 = 7

n = 12+d = 7 = 19

m+n = 5+19 = 24

Whenever in doubt, or if you get stuck, it helps to come up with actual numeric values to hopefully clear things up.

-----------------

An alternative way to get the answer:

Let's try to determine what m+n is actually saying. We have 12 right in the middle of the first term (m) and third term (n). Because the gap between the numbers is the same (that being d), we know that 12 is the midpoint of m and n. It might help to draw out a number line to see what's going on.

The midpoint of m and n is (m+n)/2

Set this equal to 12 and isolate the "m+n"

(firstTerm+thirdTerm)/2 = second term

(m+n)/2 = 12

m+n = 2*12

m+n = 24

So in general, if the first three terms of the arithmetic sequence are m, k, n, then m+n = 2k.

3 0
3 years ago
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