If one of the sides of a right triangle has length of 10, which of the

Question

If one of the sides of a right triangle has length of 10, which of the following could be the length of other two sides of the triangle?

I. 6 and 8
II. 15/2 and 25/2
III. 40/3 and 50/3

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) I, II and III

nidhihiremath · Answer

The answer should be E - I,II & III

SaquibHGMATWhiz · Answer

Solution:

We are asked which of the following pair can be sides of right angle triangle along with a side that has a length of 10

We know that the sides of a right-angle triangle follow the Pythagoras theorem which states  hypotenuse^2=base^2+perpendicular^2

I. 6 and 8

If 6, 8 and 10 are sides of a right-angle triangle, then 10 has to be the hypotenuse because it is the largest

and  10^2=6^2+8^2  has to satisfy which it does 
 ⇒100=100

II. 15/2 and 25/2

If  \frac{15}{2} ,  \frac{25}{2}  and 10 are sides of a right-angle triangle, then  \frac{25}{2}  has to be the hypotenuse because it is the largest

and  (\frac{25}{2})^2=(\frac{15}{2})^2+10^2  has to satisfy which it does 
 ⇒\frac{625}{4}=\frac{625}{4}

III. 40/3 and 50/3

If  \frac{40}{3} ,  \frac{50}{3}  and 10 are sides of a right-angle triangle, then  \frac{50}{3}  has to be the hypotenuse because it is the largest

and  (\frac{50}{3})^2=(\frac{40}{3})^2+10^2  has to satisfy which it does 
 ⇒\frac{2500}{9}=\frac{2500}{9}

Thus, we see that all the three pairs can be the sides of right angle triangle

Hence the right answer is    Option E

Vandanaa · Answer

Using Pythagorean theorem is one way to go about it, but here is one alternative :

The only piece of information we are given in question is one side of triangle 10, so lets move on to choices.

I.  10 (given), 6 and 8  - Scale down the triangle by  dividing by 2  we get  Pythagorean triplets - 5,3,4  (Yes, could be)

II.  10(given), 15/2 and 25/2  - Scale up by  multiplying by 2  to covert in whole number  (20, 15, 25)  and again scale down by  dividing by 5 , we get -  Pythagorean triplets - 4,3,5  (Yes, could be)

III.  10(given), 40/3 and 50/3  - Scale up by  multiplying by 3  to covert in whole number  (30,40,50)  and you may already have guessed where I am going with this, again scale down by  dividing by 10 , we get -  Pythagorean triplets - 3,4,5  (Yes, could be)

The Answer is - E

If one of the sides of a right triangle has length of 10, which of the

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GMAT Problem Solving (PS) Questions

If one of the sides of a right triangle has length of 10, which of the

Prep Toolkit

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