Question

In a parallelogram altitude is twice its corresponding base. If the area of the parallelogram is 450 sq cm, find its base.​

Answer 1

$\bf \underline{ \underline{\maltese\:Given} }$

⟹ In a parallelogram altitude is twice its corresponding base.

⟹ Area of the parallelogram = 450 cm²

$\bf \underline{ \underline{\maltese \: To \: find } }$

$\sf \implies Base \: of \: the \: parallelogram = \: ?$

$\bf \underline{ \underline{\maltese \: Solution } }$

$\sf Let \: us \: assume \: that,$

$\sf \implies Base \: of \: the \: parallelogram \: be \: x$

$\sf \implies \bf Then, \sf \: the \: altitude \: will \: be \: (2x )$

$\sf We \: know \: that,$

$\underline{ \boxed{ \sf Area \: of \: parallelogram = Base \times Altitude}}$

$\sf Substitute \: the \: values,$

$\sf Area \: of \: parallelogram = (x) \times (2x)$

$\implies \sf 450 = 2x^{2}$

$\implies \sf x^{2} = \dfrac{450}{2}$

$\implies \sf x^{2} = 225$

$\implies \sf x = \sqrt{225}$

$\implies \sf x = 15$

$\bf \underline{ Now},$

$\sf \implies{ \underline{\boxed{ \sf The \: base \: of \: the \: parallelogram \: (x) = \bf 15 \: cm}}}$

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$\bf \underline{ \underline{\maltese \: Varification } }$

To verify the answer just write 15 in place of x.

$\sf Area \: of \: parallelogram = (x) \times (2x)$

$\sf \implies450 = (x) \times (2x)$

$\sf \implies450 = (15) \times (2 \times 15)$

$\sf \implies450 = 15 \times 30$

$\sf \implies450 = 450$

LHS and RHS are equal.

$\bold{\longrightarrow}\:\large{\tt \red{Hence\:Verified\:!}}$