Triangle A & Triangle B are SIMILAR with there area 2023 u

Let x be the height of triangle A and y be the height of triangle of B.
since triangles are similar, ratio of area of A and B is in the ratio of x^2/y^2
Therefore, (x^2/y^2)=2023/2527
(x^2/y^2)=(17*17*7)/(19*19*7)
(x^2/y^2)=17^2/19^2
x/y=17/19

Ans=B

You need to take a hint from given options to find factors of 2013 and 2527.

my concept here was correct , but while calculating the proportion i marked a) 9: 10 because this was the closest approximation that was possible.

Can some one tell me why this approximation is not correct and whether GMAT will have such closeness in the answer choices??

Conceived to find factors of 2023 and 2527. They are not divisible by 2, 3, 5. So, it cannot be A,C,E. One should test for 17 to be a factor. It is factor of 2023, so answer is B

If the ratio of sides of a similar triangle is a/b, the ratio of their area is (a/b)^2.
Given that the ratio of area is 2023/2527, the ratio of sides will be \(\sqrt{2023/2527} = \sqrt{289/361} = 17/19\)

Answer (B)

2023 & 2527 have 7 as there factor; Once 7 is removed, they become perfect squares of 17 & 19 respectively.

Approximation is hardly required here....

Karishma I am not very good at geometry, can you explain the term 'similar traingle' and why is that if ratio of sides of a similar triangle is a/b, the ratio of their area is (a/b)^2?? Thanks in advance

B .

I went throught the following approach.Hope it helps all (experts and novice)

area of 1st traingle =1/2*a*b=2023
area of 2nf traingle=1/2*A*B=2527

the traingles are similar and so their ratio must be there i.e. 1/2*a*b / 1/2*A*B or simply a*b/A*B

So now we check every option for the factors of numerator,denominator or both.

E is clearly out because 5 isnt divisible.Same is with denominator for option A.

Same goes with all options until we get to b which is clearly divisible and the only option.

Hope it helps.


-h

i straight away calculated sqrt 0f 2023 and 2527 ,
2023 is near to 45 and 2527 near to 50 so i pickd the numbers and 45:50 is what i got.
what was wrong with this approach.

i know it should be wrong but just want to know why.

thanks

jerry

"It is due to such closeness in the answer choices" You mentioned in your earlier post that's correct

9:10 is yielded by approximation, however 17:19 is the perfect answer.

What I feel is "perfect" answer would take precedence over "Approximation". Rest, let the experts decide.....

Two triangles are similar when the ratio of their corresponding sides is constant and their corresponding angles are equal. e.g. both triangles might have angles 50-60-70. Basically one triangle will be a proportionally enlarged version of the other. There are various rules that help you recognize similar triangles such as AAA - (if all three angles of two triangles are equal, they are similar), SSS - (if the ratio of the sides is the same, they are similar), SAS (if ratio of two sides is the same and the included angle is equal), RHS (if both triangles are right angled and their hypotenuse and any one side have the same ratio). If any one rule is satisfied, the two triangles will be similar.

Check out these posts for an explanation of why ratio of areas of two triangles much be square of the ratio of their sides:

https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/03 ... -the-gmat/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2014/03 ... -the-gmat/

Also, I would suggest you to check out the important similar triangles concept from a good GMAT geometry book.

If 2 triangles are similar the ratio of their areas is equal to the ratio of squares of their corresponding sides/altitudes.

Hence (Altitude1: Altitude2)^2 = Area1:Area2 = 2023:2527 = 7*17*17 : 7*19*19 = 17^2 : 19^2 = (17:19)^2

=> Altitude1: Altitude2 = 17:19

Answer: B

the ratio is simple but the calculation really intense. without a calculator, how could you guys make it so fast?

hm, didn't know that if the triangles are similar and if the ratio of the sides is x/y then the ratio of the areas will be x^2/y^2.
i actually solved the other way, and took me some time since I had to check for the prime factors of each number:
2023 = 7*17*17
2527 = 3*19*19

since we have 17 and 19, I took a guess and chose B. other numbers do not fit.
7*17 is some three digit number
3*19 = 57.
since the two numbers do not share any common factor, and since we do not have any answer choices with three digits in it, it must be B.

Excellent Question.
Here is what i did on this one ->

As it a PS question => It can only have one answer.
Let us assume that the two triangles are right triangles.

So the ratio of their heights => Ratio of their sides.

For any two similar triangles if the side ratio is K then the area ratio is k^2


So k^2=2023/2527 => 289/361
Hence k^2=17^2/19^2

=> k=17/19

Hence the ratio of their heights must be 17:19

SMASH THAT B.

This question just looks scary because of the numbers involved.After dividing both the numerate and the denominator by 7 its is straightforward.

a/b=x/y
ay=bx

ab=2*2023
xy=2*2527
a=4046/b
x=5054/y

4046 y/b = 5054 b/y
4046 y^2 = 5054 b^2
y^2/b^2 = (7*361)/(7*289) <--- Those square roots
y/b = 17/19
Answer B

↧↧↧ Weekly Video Solution to the Problem Series ↧↧↧



Theory: If Two Triangles are Similar then ratio of their Areas is equal to square of ratio of their heights

Given that △ A and △ B are similar with areas 2023 and 2527 respectively

Let height of △ A is Ha and Height of △ B be Hb

=> \(\frac{Area Of △ A }{ Area Of △ B} = (\frac{Ha }{ Hb})^2\)
=> \((\frac{Ha }{ Hb})^2\) = \(\frac{2023}{2527}\) = \(\frac{7*17^2}{7*19^2}\) = \((\frac{17}{19})^2\)
=> \(\frac{Ha}{Hb}\) = \(\frac{17}{19}\)

So, Answer will be B
Hope it helps!

Watch the following video to learn the Basics of Similar Triangles