Math
posted by Solta .
A right triangle is formed in the first quadrant by the x and yaxes and a line through the point (3,2). write the length L of hypotenuse as a function of x.

Let the xintercept of the line be (x,0)
let the yintercept of the line be (0,y)
we have similar triangles, and by ratios ...
y/x = 3/(x2)
xy  2y = 3x
y(x2) = 3x
y = 3x/(x2)
L^2 = x^2 + y^2
= x^2 + [3x/(x2)]^2
= x^2 + 9x^2/(x^2  4x + 4)
Respond to this Question
Similar Questions

calculus
If a tangent line is drawn to the parabola y = 3  x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least are? 
Calculus
If a tangent line is drawn to the parabola y = 3  x^2 at any point on the curve in the first quadrant, a triangle is formed with the axes. At what point on the curve should the tangent be drawn to form a triangle of least area? 
Precalculus!
So I have this major assignment due, and I cant seem to figure this one out: A right triangle is formed in the first quadrant by the x and yaxes and a line through the point (5, 3). Write the length L of the hypotenuse as a function … 
math
A right triangle is formed in the first quadrant by the x and yaxes and a line through the point (2,3). Draw a figure that illustrates the problem. What is the area of the triangle A as a function of the xintercept of the line? 
calculus
a right triangle is formed in the first quadrant by the x and y axes and a line through the point (1,2). write the length of the hypotenuse as a function of x. find the vertices of the triangle such that its area is a minimum. 
Calculus
A right triangle is formed in the first quadrant by the x and yaxes and a line through the point (8,4). Write the length L of the hypotenuse as a function of x. Completely stuck came up with the sqrt(x^2+Y^2)=L, not sure what to … 
calculus
Find the point on the curve y =2/3 〖√(18x^2 )〗 (first quadrant) where a tangent line may be drawn so that the area of the triangle formed by the tangent line and the coordinate axes is a minimum. 
Mathcheck my answers please :)
1.Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15*** D.225 2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg. … 
Math
1.Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15*** D.225 2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg. … 
MATH
1.Find the length of the hypotenuse of a right triangle with the legs of 9cm and 12cm A.8 B.21 C.15*** D.225 2.The length of a hypotenuse of a right triangle is 13cm. The length of one leg is 5cm. Find the length of the other leg. …