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The hypotenuse of a right triangle is 10 cm. What .....

by factor26 » Sat Dec 03, 2011 10:15 am
The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1) The area of the triangle is 25 square centimetres.

(2) The 2 legs of the triangle are of equal length

OG ANSWER IS D BUT MY ANSWER WAS B .... CAN SOMEONE PLEASE EXPLAIN HOW STATEMENT 1 IS SUFFICIENT?

MANY THANKS!
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by kanwar86 » Sat Dec 03, 2011 10:33 am
factor26 wrote:The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1) The area of the triangle is 25 square centimetres.

(2) The 2 legs of the triangle are of equal length

OG ANSWER IS D BUT MY ANSWER WAS B .... CAN SOMEONE PLEASE EXPLAIN HOW STATEMENT 1 IS SUFFICIENT?

MANY THANKS!
x^2+y^2= 100 (Pyth Theorem).....1)
2xy=100.........................2)
Adding 1) and 2)
(x+y)^2= 200
or x+y=10 sqroot 2 (Hence statement 1 is sufficient)
or Perimeter = x+y+10 = 10(1+sq.rt2)
Statement 2. 2x^2=100; x=5 sqrt2
Perimeter = 10 (1+sqrt2)..(Hence, statement 2 is sufficient)
As both statements are sufficient. Hence, D is the correct answer
Regards

Kanwar

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by factor26 » Sat Dec 03, 2011 2:29 pm
still lost ... can you please explain in further detail? thanks
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by kanwar86 » Sat Dec 03, 2011 2:38 pm
kanwar86 wrote:
factor26 wrote:The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1) The area of the triangle is 25 square centimetres.

(2) The 2 legs of the triangle are of equal length

OG ANSWER IS D BUT MY ANSWER WAS B .... CAN SOMEONE PLEASE EXPLAIN HOW STATEMENT 1 IS SUFFICIENT?

MANY THANKS!
x and y are the two other sides of a right angled triangle
x^2+y^2= 10^2 (Pyth Theorem).....1)
2xy=100.........................2) (As 1/2(x*y)= Area of triangle, multiplying the equation by 4)
Adding 1) and 2)
x^2+y^2+2xy= 100+100
(x+y)^2= 200 (As (x+y)^2 = x^2+y^2+2xy)
or x+y=10 sqroot 2 (Hence statement 1 is sufficient)
or Perimeter = x+y+10 = 10(1+sq.rt2)
Statement 2. 2x^2=100; x=5 sqrt2 (In pythagoras theorem put x=y)
Perimeter = 2x+10 = 10+10sqrt2 =10 (1+sqrt2)..(Hence, statement 2 is sufficient)
As both statements are sufficient. Hence, D is the correct answer
Hope that helped!
Regards

Kanwar

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by pemdas » Sat Dec 03, 2011 3:27 pm
a,b,c are the sides of right triangle and c is hypotenuse
Pythagorean theorem applies as a^2+b^2=c^2. Algebraic translation (a+b)^2-2ab=c^2
since st(1) gives the area of triangle=25 (the area is equal to ab/2, where a or b is height and other side is a base)
2ab=4*(ab/2)=4*25=100 and (a+b)^2-100=c^2.
From the question stem we know c=10 and c^2=100
(a+b)^2-100=100, (a+b)^2=200, a+b = sqroot(200) and (a+b+c)= sqroot(200)+10
Perimeter (a+b+c) = 10*sqroot(2) + 10 OR 10 [sqroot(2) +1]
st(1) Sufficient
factor26 wrote:The hypotenuse of a right triangle is 10 cm. What is the perimeter, in centimeters, of the triangle?

(1) The area of the triangle is 25 square centimetres.

(2) The 2 legs of the triangle are of equal length

OG ANSWER IS D BUT MY ANSWER WAS B .... CAN SOMEONE PLEASE EXPLAIN HOW STATEMENT 1 IS SUFFICIENT?

MANY THANKS!
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