the perimeter of a parallelogram is 88 cm and one of its adjacent sides is longer than the other by 10 cm. Find the length of each of its sides
Let long side = S (cm)
then short side = S-10 (cm)
A parallelogram has opposite sides of equal length, therefore the perimeter equals
2(S + (S-10))=4S-20
We were given the perimeter is 88 cm, therefore
4S-20=88
Solve for S (the long side) and S-10 (the short side).
S= 27
S-10= 17
To find the length of each side of the parallelogram, we need to set up equations based on the given information:
Let the length of the shorter side be x cm.
Then, the length of the longer side would be (x + 10) cm.
Since a parallelogram has opposite sides equal in length, we know that the other pair of adjacent sides would also have lengths x cm and (x + 10) cm.
The perimeter of a parallelogram is calculated by adding the lengths of all its sides:
Perimeter = Length of side A + Length of side B + Length of side C + Length of side D
In this case, since we only have two adjacent sides, we can write the equation as follows:
88 cm = x cm + (x + 10) cm + x cm + (x + 10) cm
Now, let's solve the equation to find the length of each side:
Combine like terms:
88 cm = 4x + 20 cm
Subtract 20 cm from both sides:
68 cm = 4x
Divide both sides by 4:
x = 17 cm
So, the shorter side of the parallelogram is 17 cm, and the longer side is (17 + 10) cm = 27 cm.
Therefore, the length of each side of the parallelogram is 17 cm and 27 cm.
S= 17
S-10= 7
correct?