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In a parallelogram two adjacent sides are in the ratio 2:3 and the perimeter is 60┬аcm. The length of each of the two shorter sides of this parallelogram is:
12 cm
13 cm
19 cm
18 cm
12 cm
Divide half the perimeter (semi-perimeter) by the sum of ratio parts: 60/2=30. Total parts = 2+3=5. One part = 30/5=6. The shorter side corresponds to 2 parts, so 2├Ч6=12 cm.
Ratio of adjacent sides is 2:3, Perimeter of the parallelogram is 60 cm.
Perimeter=2├Ч(length+width)
Divide half the perimeter (semi-perimeter) by the sum of ratio parts: 60/2=30. Total parts = 2+3=5. One part = 30/5=6. The shorter side corresponds to 2 parts, so 2├Ч6=12 cm.
Many students mistake the perimeter formula for P=length+width instead of 2├Ч(length+width) or forget to divide the perimeter by 2 first.
Define variables based on ratio
Let the two adjacent sides be 2x and 3x cm.
Sides=2x,3x
Apply the perimeter formula
The perimeter of a parallelogram is given by 2(a+b), where a and b are adjacent sides. Setting this equal to 60 cm:
2(2x+3x)=60
Solve for x
Simplifying the equation: 2(5x)=60тЯ╣10x=60. Thus, x=6.
x=1060тАЛ=6
Calculate the shorter side
The shorter side is 2x. Substituting x=6, we get 2├Ч6=12 cm.
Side=2├Ч6=12┬аcm
A is correct because calculating the value of the ratio parts leads to a shorter side of 12 cm.
This ratio method is a fundamental skill for solving problems involving areas, perimeters, and angles in various geometric figures like rectangles and triangles.
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