Question

the area of a parallelogram is 640 square centimetre. Find the height and the base if its base is four times its corresponding height​

Answer 1

Hey mate ,

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Answer 2

$\huge\mathbb{SOLUTION:-}$

$\bold{Given:-}\begin{cases}\sf{Area\:of\:parallelogram=640cm{}^{2}}\\ \sf {base=4\times height}\end{cases}$

• Let the height of parallelogram be x
• then base becomes 4x
• And we know that the area of parallelogram

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

• Now

$\bf\underline{\underline{Step\:By\:Step\: Explanation:-}}$

$\sf\implies 4x\times x=640\\ \\ \sf\implies 4x{}^{2}=640\\ \\ \sf\implies x=\cancel{\frac{640}{4}}\\ \\ \sf\implies x=\sqrt{160}\\ \\ \sf\implies x=\sqrt{2\times 2\times 2\times 2\times 10}\\ \\ \sf\implies x=4\sqrt{10}\\ \\ \tt\longrightarrow The\:value\:of\:\sqrt{10}=3.162 \\ \\ \sf\implies x=4\times 3.162\\ \\ \sf\implies x=12.648\:\: or\:\:12.65 {\sf{\:By\:\: Estimation}}$

• The value of x is 12.65cm

• which is the height of parallelogram.

• Now the base which is 4 times height

• 4×12.65=50.6cm

$\boxed{\sf{\purple{Base=50.6cm}}}$

$\boxed{\sf{\purple{Height=12.65cm}}}$

• Let's verify:-

$\underline{\boxed{\sf{\red{VERIFICATION:-}}}}$

$\sf\implies Area=base\times height\\ \\ \sf\implies 640=50.6\times 12.65\\ \\ \sf \implies 640=640\\ \\ \sf\leadsto\:\:\:\: L.H.S=R.H.S\:$