If the lengths of three sides of an isosceles trapezium are 10 cm, 5 cm and 4 cm, its perimeter CANNOT be

23 cm

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25 cm

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29 cm

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31 cm

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Solution

The correct option is D 31 cm
In an isoscles trapezium, the non - parallel sides are equal.
As the lengths of parallel sides are not mentioned, they can take any two values of the given sides.
Consider a trapezium ABCD in which AB and CD are parallel.
(i) AB = 10 cm, CD = 4 cm, BC = 5 cm
AD = BC = 5 cm
Perimeter = AB + BC + CD + AD = 10 + 5 + 4 + 5 = 24 cm

(ii) AB = 10 cm, CD = 5 cm, BC = 4 cm
AD = BC = 4 cm
Perimeter = AB + BC + CD + AD = 10 + 5 + 4 + 4 = 23 cm

(iii) AB = 4 cm, CD = 5 cm, BC = 10 cm
AD = BC = 10 cm
Perimeter = AB + BC + CD + AD = 10 + 5 + 4 + 10 = 29 cm

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