SOLUTION: Hello! May you help me with this question? If the hypotenuse of a right triangle is 10 and one leg is 5 radical 3, then the area if the triangle is... (A) 5 (B) 25 radical 3 (C

Algebra ->  Pythagorean-theorem -> SOLUTION: Hello! May you help me with this question? If the hypotenuse of a right triangle is 10 and one leg is 5 radical 3, then the area if the triangle is... (A) 5 (B) 25 radical 3 (C      Log On


   

Question 499042: Hello! May you help me with this question?
If the hypotenuse of a right triangle is 10 and one leg is 5 radical 3, then the area if the triangle is...
(A) 5
(B) 25 radical 3
(C) 25
(D) 50 radical 3
(E) 12.5 radical 3
This is what i did to try to solve the problem. So according to Pythagorean theorem I did this formula a(squared)+b(squared)= c(squared). Since the hypotenuse is always c and one leg is 5 radical 3, this is what i did a(squared)+ 5 radical 3(squared)= 10(squared). which equals a(squared)+ 15= 100.
this can be simplified to a(squared)=85. so a is the square root of 85. since this is the height, and 5 radical 3 is the base i multiply radical 85 times 5 radical 3. which is 5 radical 255. then i divide this by 2 and get 2.5 radical 255. but this is not one of the choices. May you tell me what you got and how please? :) thank you
By, Nang Tun
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
You have to square 5sqrt(3). What you did was square (sqrt3) then multiply by 5.

By the Pythagorean theorem, a would therefore be





You can also find a by noting that this is a 30-60-90 triangle.

The area of the triangle is 5(5sqrt(3))/2 = 12.5(sqrt3).