Solving Problems on the Properties of Parallelograms
GRADE 9 – LEAP 3RD QUARTER
Step-by-step explanation:
X = 6
AB = 13 cm
y = 10
AD = 13 cm
Perimeter = 52 cm
Step-by-step explanation:
(I have a feeling that you got your measurements wrong. I noticed that you put CD=(x-7)cm when you might mean CD = (x+7)cm since “=” and “+” are on the same key. For now I shall assume that you meant CD= (x+7)cm)
One of the properties of a parallelogram is that it has congruent opposite sides. In parallelogram ABCD, AB=CD and BC=AD.
We are given the sides of the parallelogram. We can substitute the values and equate the opposite sides.
AB = CD
3x − 5 = x + 7
3x – x = 7+5
2x = 12
x = 6
We have x = 6.
AB – 3x – 5
AB
3(6) – 5
AB 18-5
AB = 13
AB is 13 cm. Since AB = CD; CD is also 13 cm.
Let us do the other pair of opposite sides, BC and AD. They are also equal to each other.
BC = AD
2y7= y + 3
2y-y = 7+3
y = 10
We have y = 10.
AD = y + 3
AD 10+ 3
AD = 13
AD is 13 cm. Since AD = BC; BC is also 13 cm.
The perimeter of a polygon is the sum of the measures of all its sides. To get the perimeter of parallelogram ABCD, we add the measures of all its sides.
Perimeter (ABCD) = AB + BC+CD+CD
Perimeter (ABCD) 13+13+13 + 13
Perimeter (ABCD) = 52
The perimeter of Parallelogram ABCD is 52 cm.
To know more about parallelograms, click here
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