In parallelogram ABCD,AB = 20 , cm. Altitudes | vedclass

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Question

(A) The area of a parallelogram is given by the formula $	ext{Area} = 	ext{base} 	imes 	ext{corresponding altitude}$.For base $AB = 20 \, cm$ and

Vedclass · Accepted Answer

$BC = 16 \, cm, 	ext{ Perimeter} = 72 \, cm$

Vedclass · Answer

(A) The area of a parallelogram is given by the formula $	ext{Area} = 	ext{base} 	imes 	ext{corresponding altitude}$.For base $AB = 20 \, cm$ and corresponding altitude $DX = 12 \, cm$,the area is:$	ext{Area} = AB 	imes DX = 20 \, cm 	imes 12 \, cm = 240 \, cm^2$.Since the area is constant,for base $BC$ and corresponding altitude $AY = 15 \, cm$,we have:$	ext{Area} = BC 	imes AY = 240 \, cm^2$.$BC 	imes 15 \, cm = 240 \, cm^2 \implies BC = \frac{240}{15} \, cm = 16 \, cm$.The perimeter of a parallelogram is $2 	imes (	ext{sum of adjacent sides})$.$	ext{Perimeter} = 2 	imes (AB + BC) = 2 	imes (20 \, cm + 16 \, cm) = 2 	imes 36 \, cm = 72 \, cm$.

In parallelogram $ABCD$,$AB = 20 \, cm$. Altitudes $AY$ and $DX$ are corresponding to bases $BC$ and $AB$ respectively. If $DX = 12 \, cm$ and $AY = 15 \, cm$,then find $BC$ and the perimeter of $ABCD$.

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