The sides of a right triangle are consecutive even integers, and the l

Question

The sides of a right triangle are consecutive even integers, and the length of the longest side is p. Which of the following equations could be used to find p?

A. (p–4)^2=p^2–(p−2)^2
B. (p–2)^2=(p–4)–p^2
C. p^2+4^2+2^2=6^2
D. (p–2)^2=p^2–(p−1)^2
E. (p+2)^2+(p+4)^2=p^2

ShristiK · Answer

The sides are consecutive EVEN integers. 
So, if longest side has a length of p, the other two sides will be (p-2) and (p-4)
And using the Pythagorean Theorem, we get: p^2 = (p-2)^2 + (p-4)^2

Ans: A

HolaMaven · Answer

If sides are three consecutive even integers, the right triangle in talk can have sides 6,8,10 where value of largest side p=10
thus working on all options
A - (10-4)^2 = 10^2 - (10-2)^2 / 6^2 = 10^2 - 8^2 which is true
B - (10-2)^2 = (10-4)^2 - 10^2 / 8^2 = 6^2 - 10^2which is false 
C - 10^2 + 4^2 + 2^2 = 6^2 which is false
D - (10-2)^2 = 10^2 - (10-1)^2 / 8^2 = 10^2 - 9^2which is false
E - (10+2)^2 + (10+4)^2 = 10^2 / 12^2 + 14^2 = 10^2which is false
Thus answer is option A

mamun2871 · Answer

The sides of a right triangle are consecutive even integer and the longest side is P. So, other sides are p-2 & p-4. Using Pythagorean theory p^2=(p-2)^2+(p-4)^2 , => (p-4)^2=p^2-(p-2)^2.
Answer is A.

GMATinsight · Answer

One can use the wisdom for GMAT that GMAT uses only specific cases of right angle triangles 3-4-5 being the most frequently used pythagorean triplet

Here three consecutive even integers will be second multiple of 3-4-5 i.e. 6-8-10

As give, p = 10
p-2 = 8
p-4 = 6

Now check options

Option A:  (p–4)^2=p^2–(p−2)^2  i.e.  6^2 = 10^2 - 8^2  fits well hence

Answer: Option A

Abhishek009 · Answer

Base < Altitude < Hypotenuse

So,  p - 4 < p - 2 < p

Now,  p^2 = ( p - 2 )^2 + ( p - 4 )^2   { Pythagorus Theorem }

Thus, Answer must be (A)

BrentGMATPrepNow · Answer

GIVEN: p = length of the longest side

Since the side lengths are  consecutive even integers , we can say: 
p - 2 = length of the 2nd longest side
p - 4 = length of the shortest side

NOTE: The longest side is the HYPOTENUSE. 
So, p = length of the HYPOTENUSE
And p - 2 = length of one leg of the right triangle 
And p - 4 = length of the other leg of the right triangle

By the Pythagorean Theorem, we can write: (p - 2)² + (p - 4)² = p²
Check the answers . . . not there! Looks like we need to fiddle with the equation to make it look like on of the answer choices.

Take: (p - 2)² + (p - 4)² = p²
Subtract (p - 2)² from both sides to get: (p - 4)² = p² - (p - 2)² . . . BINGO!!

Answer: A

Cheers,
Brent

MathRevolution · Answer

Consecutive even integers: 2, 4 and 6

Right angles triangle: Longest side is p{6}.

Then, the other two sides are (p - 2) and (p - 4)

=>  p^2 = (p - 2) ^2 + (p - 4)^2

OR =>  p^2 - (p - 2) ^2 = (p - 4)^2

Answer A

bumpbot · Answer

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The sides of a right triangle are consecutive even integers, and the l

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