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Geometry Level 3

If each of the two dimensions of a rectangle is increased by 100%, by what percentage is the area increased?

200% 300% 400% 100%

Deva Craig by Deva Craig , 22, USA

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1 solution

Let a a be the area of the original rectangle and A A be the area of the bigger rectangle. Then we have

a A = L W ( 2 L ) ( 2 W ) = L W 4 L W = 1 4 \dfrac{a}{A}=\dfrac{LW}{(2L)(2W)}=\dfrac{LW}{4LW}=\dfrac{1}{4}

A = 4 a A=4a

% i n c r e a s e d = ( 4 − 1 ) ( 100 % ) = \%~increased=(4-1)(100 \%)= 300 % \boxed{300 \%}

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nice solution

Ramiel To-ong - 2 years, 4 months ago

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