<h3>Question:</h3>
The length of a rectangle is 6 metres more than its breadth. the perimeter of the rectangle is 60 metres . find the length and breadth of the rectangle.
<h3>To find:</h3>
<h3>Given:</h3>
- length of a rectangle is 6 metres more than its breadth
- perimeter = 60 m
<h3>Let:</h3>
<h3>Answer:</h3>
We know:
<u>Perimeter = 2(L+B)</u>
by using this formula we can find value of x.
![: \implies \sf60 = 2(x + x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf60%20%3D%202%28x%20%2B%20x%20%2B%206%29)
![: \implies \sf \dfrac{60}{2} = (x + x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%20%5Cdfrac%7B60%7D%7B2%7D%20%20%3D%20%28x%20%2B%20x%20%2B%206%29)
![: \implies \sf \dfrac{ {\cancel{60}}^{ \: 30} }{ {\cancel{2}}^{ \: 1}} = (x + x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%20%5Cdfrac%7B%20%20%7B%5Ccancel%7B60%7D%7D%5E%7B%20%5C%3A%2030%7D%20%7D%7B%20%7B%5Ccancel%7B2%7D%7D%5E%7B%20%5C%3A%201%7D%7D%20%20%3D%20%28x%20%2B%20x%20%2B%206%29)
![: \implies \sf 30 = (x + x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%2030%20%3D%20%28x%20%2B%20x%20%2B%206%29)
![: \implies \sf 30 = (2x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%2030%20%3D%20%282x%20%2B%206%29)
![: \implies \sf 30 - 6 = 2x](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%2030%20-%206%20%3D%202x%20)
![: \implies \sf 24 = 2x](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%2024%20%3D%202x%20)
![: \implies \sf x = \frac{24}{2} \\](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%20x%20%20%3D%20%20%5Cfrac%7B24%7D%7B2%7D%20%20%5C%5C%20)
![: \implies \sf x = \frac{ {\cancel{24}}^{ \: 12} }{ {\cancel{2}}^{ \: 1} } \\](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf%20x%20%20%3D%20%20%5Cfrac%7B%20%20%7B%5Ccancel%7B24%7D%7D%5E%7B%20%5C%3A%2012%7D%20%7D%7B%20%20%7B%5Ccancel%7B2%7D%7D%5E%7B%20%5C%3A%201%7D%20%7D%20%20%5C%5C%20)
![: \implies \star \boxed{ \sf x = 12} \star](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Cstar%20%5Cboxed%7B%20%5Csf%20x%20%20%3D%2012%7D%20%5Cstar)
Let's Verify whether value of x is correct or not
![: \implies \sf60 = 2(x + x + 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf60%20%3D%202%28x%20%2B%20x%20%2B%206%29)
insert Value of x
![: \implies \sf60 = 2(12 + 12+ 6)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf60%20%3D%202%2812%20%2B%2012%2B%206%29)
![: \implies \sf60 = 2(30)](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Csf60%20%3D%202%2830%29)
![: \implies \star \boxed{ \sf60 = 60} \star](https://tex.z-dn.net/?f=%20%3A%20%20%5Cimplies%20%5Cstar%20%5Cboxed%7B%20%5Csf60%20%3D%2060%7D%20%5Cstar)
![\large \dag \bigg( \large \sf{}LHS = RHS \bigg) \dag](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cdag%20%5Cbigg%28%20%5Clarge%20%5Csf%7B%7DLHS%20%3D%20RHS%20%5Cbigg%29%20%5Cdag)
Hence verified
First let's find value of length :
- Length = 6+x
- Length =6+12
- <u>L</u><u>ength = </u><u>18</u><u> </u><u>cm</u>
Now Let's find value of breadth:
- Breadth = x
- <u>B</u><u>readth = 12</u><u> </u><u>cm</u>
If three times the sum of eight and a number is sixty, then you need to break it down to write it out. First, we know we're multiplying 3 * (times) something. That something is 8 and a number, or x. So it'd be 8 + x. So we have 3 * (8 + x). And we know that equals 60, so we have 3 * (8 + x) = 60
The sum of angles in a regular octagon is
180*(8 - 2) = 1080°.
Each angle of the octagon is 1080/8 = 135°.
There are 8 equal central angles to each vertex.
Each central angle is 360/8 = 45°
Answer:
Therefore the octagon will map onto itself if it is rotated by its center through these angles:
45°
90°
135°
180°