The sides of parallelogram 2x+y,3y-2x,5y-8,4x-3 are given in cm.find x and y and the perimeter of the parallelogram
I assume you have listed the sides in order going around the parallogram.
Opposite sides are equal, so ...
2x+y = 5y-8 ----> 2x-4y = -8
3y-2x = 4x-3 ---> 6x - 3y = 3
divide the 2nd by 3
2x - y = 1
2x-y = 1
2x-4y = -8
subtract them
3y = 9
y = 3
then 2x-3=1
x = 2
for perimeter, evaluate each of the sides using the values for x and y, then add up the length of the sides.
24cm
I've replied
The sydes of parallelogram in fig 14.6are giving in cm with the breath of 3y+2x and the other breath of 4x-3
Hey there! Let's solve this with a touch of humor, shall we?
To find x and y, we'll set up a system of equations using the given sides of the parallelogram.
Given:
Side 1: 2x + y = cm
Side 2: 3y - 2x = cm
Side 3: 5y - 8 = cm
Side 4: 4x - 3 = cm
Now, let's solve for x and y using these equations. Just bear with me, we're entering equation-solving territory!
Multiplying the first equation by 2:
4x + 2y = cm
Adding the second equation to this:
4x + 2y + (3y - 2x) = cm
2y + 3y = cm
5y = cm
y = (1/5)cm
Plugging the value of y back into the first equation:
2x + (1/5)cm = cm
2x = (4/5)cm
x = (2/5)cm
So, our thrilling conclusion is:
x = (2/5)cm
y = (1/5)cm
But wait, the fun doesn't end there! We still need to find the perimeter of this marvelous parallelogram.
Perimeter = 2 * (Side 1 + Side 2)
Perimeter = 2 * [(2x + y) + (3y - 2x)]
Perimeter = 2 * (2x + 3y)
Plugging in the values of x and y we found:
Perimeter = 2 * [(2 * (2/5)cm) + (3 * (1/5)cm)]
Perimeter = 2 * [(4/5)cm + (3/5)cm]
Perimeter = 2 * [(7/5)cm]
Perimeter = (14/5)cm
And there you have it! The perimeter of the parallelogram is (14/5) cm. I hope this answer brought a smile to your face, even if it's just a "geometry" smile!
To find the values of x and y, we need to solve the system of equations formed by equating the given sides.
1) 2x + y = 3y - 2x [Equation 1]
2) 5y - 8 = 4x - 3 [Equation 2]
To eliminate one variable, we can rearrange Equation 1 by moving all terms to one side:
4x + 2x = 3y - y - 2
6x = 2y - 2
3x = y - 1 [Equation 3]
Now we can substitute Equation 3 into Equation 2:
5y - 8 = 4x - 3
5y = 4x - 3 + 8
5y = 4x + 5 [Equation 4]
Next, we will substitute Equation 3 into Equation 4:
5(y - 1) = 4x + 5
5y - 5 = 4x + 5
5y = 4x + 10
y = (4/5)x + 2 [Equation 5]
By substituting Equation 5 into Equation 3, we can solve for x:
3x = (4/5)x + 2 - 1
3x = (4/5)x + 1
15x = 4x + 5
15x - 4x = 5
11x = 5
x = 5/11
Now that we have the value of x, we can substitute it back into Equation 5 to find y:
y = (4/5)(5/11) + 2
y = (4/11) + 2
y = (4/11) + (22/11)
y = 26/11
So x = 5/11 and y = 26/11.
To find the perimeter of the parallelogram, we add up the lengths of all four sides.
Side 1: 2x + y = (2 * (5/11)) + (26/11) = (10/11) + (26/11) = 36/11 cm
Side 2: 3y - 2x = (3 * (26/11)) - (2 * (5/11)) = (78/11) - (10/11) = 68/11 cm
Side 3: 5y - 8 = (5 * (26/11)) - 8 = (130/11) - 8 = (130/11) - (88/11) = 42/11 cm
Side 4: 4x - 3 = (4 * (5/11)) - 3 = (20/11) - (33/11) = -13/11 cm
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
= (36/11) + (68/11) + (42/11) + (-13/11)
= (133/11) cm
Therefore, the perimeter of the parallelogram is 133/11 cm.