What is the perimeter of a certain right triangle?

Question

1) The length of hypotenuse is 4
2) The area of triangle is 4.5

rohit8865 · Answer

1) no info about other sides...insuff
2) no info about hypotenuse /other sides....insuff

Combining
let base = b , height = h
then from (2) h*b/2= 4.5
h*b=9---(a)
From (1)
h= sq. root Hyp^2- b^2 =16-b^2= sq root(4+b)(4-b)
similarly b= sq root (4+h)(4-h)
putting above values of h & b in (a) we can calculate h or b (as h=9/b)

Thus all sides are known 
hence perimeter can be calculated
Suff

Ans C

Bunuel · Answer

This is a copy of the following question: what-is-the-perimeter-of-a-certain-right-triangle-221855.html

MathRevolution · Answer

==> In the original condition, for the right triangle, there are 2 variables and in order to match the number of variables to the number of equations, there must be 2 equations. Since there is 1 for con 1) and 1 for con 2), C is most likely to be the answer. By solving con 1) and con 2) and assume the two hypotenuses of the triangle as a and b, you get \(a^2+b^2=4^2=16\), and from ab/2=4.5, you get ab=9. Then, from \((a+b)^2=a^2+b^2+2ab=16+2(9)=16+18=34\), you get a+b=√34, so the perimeter of the right triangle=a+b+4=√34+4, hence it is unique and sufficient.

Therefore, the answer is C.
Answer: C

Therefore, the answer is C. 
Answer: C

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What is the perimeter of a certain right triangle?

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What is the perimeter of a certain right triangle?

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