In the given figure, ABCD is a trapezium in which AB $= 7$ cm, AD $=$ BC $= 5$ cm, DC $=$ x cm and the distance between AB and DC is $4$ cm. Then the value of x is ____________.

13

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16

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19

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Solution

The correct option is A $13$
In $△ A L D$ and $△ B M C$ :
$D L^{2} = A D^{2} - A L^{2} = 5^{2} - 4^{2} = 9 \Rightarrow L D = 3 c m$
Similarly, $M C = 3 c m$
$∴ x = D L + L M + M C$ (Length of $L M = A B = 7 c m$ )
$x = 3 + 7 + 3 = 13 c m$

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In the given figure, ABCD is a trapezium in which AB=7cm, AD=BC=5cm, DC=x cm and the distance between AB and DC is 4cm. Then the value of x is ____________.

The correct option is A 13In △ALD and △BMC:DL2=AD2−AL2=52−42=9⇒LD=3 cmSimilarly, MC=3 cm∴x=DL+LM+MC (Length of LM=AB=7 cm)x=3+7+3=13 cm

In the given figure, ABCD is a trapezium in which AB $= 7$ cm, AD $=$ BC $= 5$ cm, DC $=$ x cm and the distance between AB and DC is $4$ cm. Then the value of x is ____________.

The correct option is A $13$
In $△ A L D$ and $△ B M C$ :
$D L^{2} = A D^{2} - A L^{2} = 5^{2} - 4^{2} = 9 \Rightarrow L D = 3 c m$
Similarly, $M C = 3 c m$
$∴ x = D L + L M + M C$ (Length of $L M = A B = 7 c m$ )
$x = 3 + 7 + 3 = 13 c m$