Question

one pair of adjacent sides of a parallelogram is in ratio 3 : 4 if one of its angle , angleA is a right angle and diagonal BD =10cm , then find the length of sides of the parallelogram and perimeter of the parallelogram

Answer 1

DIAGONAL WILL BE 10cm


SIDES ARE IN RATIO 3:4

SO THE SIDES WILL BE 3x AND 4x

ONE ANGLE IS 90°

BY USING HYPOTENUSE THEORM

WE GET:

[3x]^2 + [4x]^2= [10]^2
9x^2 + 16x^2 = 100
25x^2= 100
x^2= 4
x = 2

THEN SIDES OF PARALLELOGRAM ARE 3×2=6 AND 4×2=8

Answer 2

As adjacent sides are in the ratio 3:4 .Let AD=3x and AB=4x .Applying pythagoras theorem , in △ABDAB2+AD2=BD216x2+9x2=10025x2=100x2=4x=2 cm.So ,AB=4(2)=8 cm .AD=3(2)=6 cm .CD=AB=8 cm . (Opposite sides of parallelogram)BC=AD=6 cm . (Opposite sides of parallelogram)Perimeter of parallelogrm=2 (AB+AD)=2 (8+6)=2×14=28 cm .

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