SOLUTION: The hypotenuse of a right triangle is four times its base. If B is the base of the triangle, express the area of the triangle A as a function of B. (A) A= 2b^2 (B) A= (sqrt(3)

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Question 1068027: The hypotenuse of a right triangle is four times its base. If B is the base of the triangle, express the area of the triangle A as a function of B.
(A) A= 2b^2
(B) A= (sqrt(3) b^2) /2
(C) A= sqrt(3) b^2
(D) A= 2 sqrt(15) b^2
(E) A = (sqrt(15)b^2)/2

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
h-hypotenuse
b-base
a-height
A-area
.
.
h=4b
You also know,
a%5E2%2Bb%5E2=h%5E2
a%5E2%2Bb%5E2=%284b%29%5E2
a%5E2=16b%5E2-b%5E2
a%5E2=15b%5E2
a=sqrt%2815%29b
So then the area,
A=%281%2F2%29ba
A=%281%2F2%29b%2Asqrt%2815%29b
A=%28sqrt%2815%29%2F2%29b%5E2