Triangle Problem Help

[EMAN]

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

[kholll557MBA10]

Did you not figure out the other 2 sides? I know that the equation for the area of a triangle is 1/2bh since the area is 25 we know that the (bh) has to equal 50,in order for the area to be 25.. since number (2) says that 2 of the legs are equal and we know the hypotenuse is 10, what times what will equal 50, 1*50, 2*25, 5*10. so the answer would have to be 10*5, so the sides of the triangle are 10, 10, 5, which means the perimeter is 25.

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

[umaa]

The hypotenuse of a right triangle is 10 cm. What is the perimeter, in cm, of the triangle?

(1) The area of the triangle is 25 cm squared
(2) The 2 legs of the triangle are equal in length

IMO D.

Since its a right angle triangle, we can use Pythagoras theorm.

sqrroot (a^2 + b^2) = 10

a^2 + b^2 = 100 - I

Statement 1:
Area of the triangle ab/2 = 25

ab = 50; 2ab = 100

Combine this equation with equation I,

a^2 + b^2 + 2ab = 100+100

(a+b)^2 = 200
a+b = sqrrot(200)

Since we already know c(diagonal), a+b+c = sqrrot(200)+10

So, Statement 1 is sufficient.

Statement 2:
If 2 legs of the triangle is equal, we are sure that hypotenuse is not one of the length. It should be a and b.

If both are equal, then the angle is 45:45:90.

From there, we can find a+b+c

Statement 2 is also sufficient.

OA pls.

[EMAN]

I believe you are correct. I don't have the books in front of me though. Can you explain the 2ab part of the equation? I think they mentioned that in the OG and I was a little thrown off by that.

[umaa]

We know the hypotenuse. Its 10. The triangle is right angle triangle. it means, one angle is 90 degree. hypotenuse is opposite to 90 degree.

If the other 2 sides are equal, then it means, the other two angles are equal.

180-90 =90; 90/2 = 45

So, both the angles are 45:45.

We know 45:45:90 measurements. its, xx sqrroot(2)

we know x sqrrot (2) = 10

Find x from that and then add x+x+x sqrrot(2)

thats the answer.

[EMAN]

Gotcha. Thanks.