SAT Question of the Day Nov 14th 2012

The length of a rectangle is increased by 20%, and the width of the rectangle is increased by 30%. By what percentage will the area of the rectangle be increased?

A.     25%

B.     36%

C.     50%

D.     56%

E.     60%

In order to solve this question we better have a good understanding of two concepts.

One is area – the other is %.

As usual there are many ways to solve – and I’ll walk you through a few.

AREA of a RECTANGLE – will always be the result of multiplying the length by the width (sometimes it will appear as base times the height perpendicular to that base).

PERCENTAGE – not enough word to describe the suffering students go through with this otherwise “simple” concept. In essence it is a fraction with a denominator of 100. It is always related to something (because of that we always look for % of what?).

The easy way to solve: Assume the length is 10 units – increase it by 20% out of ten and get 12 units as the length of the new rectangle. Assume the width is also 10 units. Increase it by 30% (of the 10) and get 13. 12X13=156 – this is 56 area units bigger than the original or 56% larger than the 100% of the area of the 10X10 original rectangle.

The long way to solve: L times W = original area or 100% 120% of L times 130% of W = 120/100 of L times 130/100 of W = 156/100 of W times L or 156% of W times L. This implies the new area is 156% of the original area. In other words it is equal to the original area + an addition of 56% of the original area.

 

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