The consecutive sides of a quadrilateral measure (x-17), (24-x), (3x-40) and (x+1). The perimeter is 42 cm . is the quadrilateral a parallelogram ?
Hi please will you help me thakn youu
let's see:
x-17 + 24-x + 3x-40 + x+1 = 42
4x=74
x = 74/4 = 18.5
so the sides are:
1.5, 5.5 , 15.5 , and 19.5
make a rough sketch
What do you think?
Of course! I'll be happy to help you.
To determine if the given quadrilateral is a parallelogram, we need to check if the opposite sides are parallel. In a parallelogram, opposite sides have the same length.
Let's find the length of each side of the quadrilateral using the given expressions:
Side 1: x-17
Side 2: 24-x
Side 3: 3x-40
Side 4: x+1
Next, we can write the equation for the perimeter of the quadrilateral:
Perimeter = Side 1 + Side 2 + Side 3 + Side 4
Given that the perimeter is 42 cm, we can write the equation:
42 = (x-17) + (24-x) + (3x-40) + (x+1)
Now, let's simplify the equation:
42 = x - 17 + 24 - x + 3x - 40 + x + 1
Combining like terms:
42 = 4x - 32
Now, let's solve for x:
42 + 32 = 4x
74 = 4x
Dividing both sides by 4:
x = 74/4
x = 18.5
Now that we have the value of x, we can substitute it back into the expressions for the sides to find their lengths:
Side 1 = 18.5 - 17 = 1.5 cm
Side 2 = 24 - 18.5 = 5.5 cm
Side 3 = 3(18.5) - 40 = 16.5 cm
Side 4 = 18.5 + 1 = 19.5 cm
Now, we can compare the opposite sides:
Opposite sides 1 and 3: 1.5 cm and 16.5 cm (not equal)
Opposite sides 2 and 4: 5.5 cm and 19.5 cm (not equal)
Since the opposite sides are not equal, we can conclude that the given quadrilateral is not a parallelogram.
I hope this explanation helps!