Question

EHIG is a parallelogram. Find the value of:GH= 10x + 2GJ= 7.2 - 5EJ = 37 - 2yJI = 4y - 5HECX =y=GJ =IJ =Blank 1:Blank 2:Blank 3:Blank 4:

Answer 1

Question:

Solution:

According to the figure, we have that:

`JH\text{ = GH-GJ}`

that is:

`JH\text{ = (10x+2)-(7x-5)}`

this is equivalent to:

`JH\text{ = 3x +7}`

now, the diagonals of a parallelogram bisect each other. So that, we get the following equation:

`GJ=JH`

this is equivalent to:

`7x-5=3x+7`

this is equivalent to:

`7x-3x\text{ = 7+5}`

this is equivalent to:

`4x\text{ = 12}`

solving for x, we get:

`x\text{ = }(12)/(4)\text{ = 3}`

On the other hand, remember again that the diagonals of a parallelogram bisect each other. So that, we get the following equation:

`EJ=JI`

this is equivalent that

`37-2y=4y-5`

this is equivalent to:

`4y\text{ +2y = 37+5}`

this is equivalent to:

`6y\text{ = 42}`

solving for y, we get:

`y\text{ = }(42)/(6)\text{ = 7}`

now, applying the values obtained for x and y we get:

`GJ\text{ = 7x -5 = 7(3)-5 = 16}`

and

`IJ\text{ = 4y-5 = 4(7)-5 = 23}`

we can conclude that the correct answer is:

`x\text{ = 3}`

`y\text{ = 7}`

`GJ\text{ = 16}`

`IJ\text{ = 23}`