Answer:
g
Step-by-step explanation:
<h3><u>Question:</u></h3>
The perimeter of a rectangle is 34 units. Its width W is 6.5 units.
Write an equation to represent the perimeter in terms of the length L, and find the value of L
<h3><u>Answer:</u></h3>
The length of rectangle is 10.5 units
<h3><u>
Solution:</u></h3>
Given that,
Perimeter of rectangle = 34 units
Width of rectangle = 6.5 units
Let "L" be the length of rectangle
<em><u>The perimeter of rectangle is given by formula:</u></em>
Perimeter = 2(length + width)
<em><u>Substituting the values we get,</u></em>
![34 = 2(L + 6.5)](https://tex.z-dn.net/?f=34%20%3D%202%28L%20%2B%206.5%29)
Thus the equation is found
<em><u>Solve for "L"</u></em>
![L + 6.5 = \frac{34}{2}\\\\L + 6.5 = 17\\\\L = 17 - 6.5\\\\L =10.5](https://tex.z-dn.net/?f=L%20%2B%206.5%20%3D%20%5Cfrac%7B34%7D%7B2%7D%5C%5C%5C%5CL%20%2B%206.5%20%3D%2017%5C%5C%5C%5CL%20%3D%2017%20-%206.5%5C%5C%5C%5CL%20%3D10.5)
Thus length of rectangle is 10.5 units
Step-by-step answer:
Given:
A triangle
Perimeter = 60 cm
longest side = 4* shortest side (x)
Solution:
longest side = 4x
shortest side = x
third (intermediate side = 60 -x -4x = 60-5x
The triangle inequality specifies that the sum of the two shorter sides must be greater than the longest side to form a triangle. Hence
x + y > 4x
x + 60-5x > 4x
60 - 4x > 4x
8x < 60
x < 60/8 = 7.5, or
x < 7.5
Therefore to form a triangle, x (shortest side) must be less than 7.5 cm.
Examine the options: both 7 and 5 are both less than 7.5 cm.
40, 30 and 25 all have a problem because the longest side (4 times longer) will exceed the perimeter of 60.
Now also examine cases where 4x is NOT the longest side, in which case we need
4x>=y
or
4x >= 60-5x
9x >=60
x >= 6.67
so x=5 will not qualify, because 4x will no longer be the longest side.
The only valid option is x=7 cm
The side lengths for x=7 and x=5 are, respectively,
(7, 25, 28)
5, 20, 35 (in which case, the longest side is no longer 4x=20, so eliminated)
Find a common denominator by multiplying the denominators together. Use that common denominator to create equivalent fractions. Then, compare the numerators to figure out which is bigger