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Question

The ratio of the lengths of the parallel sides of a trapezium is 3:2. The shortest distance between them is 15cm. If the area of the trapezium is 450 sq. cm. Find the sum of the lengths of the parallel sides ?

hintHint:

let the length of parallel sides be x and y (x>y).Given ratio of x:y = 3:2
Substitute the equation in the formula area of trapezium = ½ × (height)(sum of lengths
of parallel side) and equate to find x

The correct answer is: 60 cm


    Ans :- 60 cm
    Explanation :-
    Step 1:-  Find the equation between x and y  and find the sum of lengths of parallel sides in terms of y.
    let the length of parallel sides be x and y (x>y).
    Given ratio of x:y = 3:2 not stretchy rightwards double arrow x over y equals 3 over 2 not stretchy rightwards double arrow y equals 2 x divided by 3
    Sum of lengths of parallel sides = x plus y equals x plus 2 x divided by 3 equals 5 x divided by 3
    Step 2:-substitute the values in the area formula find x
    Given area of trapezium = 450 sq.cm
    Altitude (or) height = 15 cm
    area of trapezium = ½ × (height)(sum of lengths of parallel side)
    not stretchy rightwards double arrow 450 equals 1 half cross times left parenthesis 15 right parenthesis cross times open parentheses fraction numerator 5 x over denominator 3 end fraction close parentheses not stretchy rightwards double arrow 30 cross times 2 equals fraction numerator 5 x over denominator 3 end fraction not stretchy rightwards double arrow fraction numerator 5 x over denominator 3 end fraction equals 60
    We know Sum of lengths of parallel sides = x plus y equals x plus 2 x divided by 3 equals 5 x divided by 3
    So, Sum of lengths of parallel sides = 60 cm.
    Therefore, Sum of lengths of parallel sides is 60 cm.

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