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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## The length and width of a certain rectangle are in the rati tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## The length and width of a certain rectangle are in the rati [GMAT math practice question] The length and width of a certain rectangle are in the ratio 4 to 5. The area of the rectangle is 2,000 square units. If the length and width of the rectangle are both increased by 10 units, what is the increase in the area of the rectangle? A. 800 B. 900 C. 1,000 D. 1,100 E. 1,250 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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[GMAT math practice question]

The length and width of a certain rectangle are in the ratio 4 to 5. The area of the rectangle is 2,000 square units. If the length and width of the rectangle are both increased by 10 units, what is the increase in the area of the rectangle?

A. 800
B. 900
C. 1,000
D. 1,100
E. 1,250
Hi Max@Math Revolution,
Let's take a look at your question.

Since, the length and width of a certain rectangle are in the ratio 4 to 5, therefore,
Length = 5x
Width = 4x
Area = 2000 sq units

$$Area\ =\ Length\ \times\ Width$$
$$2000\ =\ \left(5x\right)\left(4x\right)$$
$$2000\ =\ 20x^2$$
$$x^2=\frac{2000}{20}=100$$
$$x=10$$

Now we can find the length and width of the rectangle:
$$Length=5x=5\left(10\right)=50$$
$$Width=4x=4\left(10\right)=40$$

If the length and width of the rectangle are both increased by 10 units, then area will be:
$$Area=\left(50+10\right)\left(40+10\right)=\left(60\right)\left(50\right)=3000$$
$$Increase\ in\ area\ =\ 3,000-2,000=1,000$$

Therefore, Option C is correct.

Hope it helps.
I am available if you'd like any follow up.

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Suppose the length is L = 4k and the width is W = 5k for some k. Then
L*W = 4k*5k = 20k^2 = 2,000.
k^2 = 100 and k = 10.
Thus, L = 4k = 40 and W = 5k = 50.
The area of the rectangle after increasing both the length and the width is (L+10)(W+10) = (40 + 10)(50 + 10) = 50*60 = 3,000 square units.
Thus, the increase in the area is 3,000 - 2,000 = 1,000 square units.

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