Write a function that gives the area of the rectangle in terms of x only

Question

A rectangle is inscribed in the triangle as shown where a = 7 and b = 10.

 

Write a function that gives the area of the rectangle in terms of x only

 

 

The rectangle is inscribed in a triangle.  The rectangle's height is y 

and the length is x. The height of the rectangle is at b and the length of triangle is at a. 

 

 

Answer 1

Hi Tori

 

The area of this rectangle is x*y. But, this problem requires that you represent the variable "y" in terms of "x" only.

 

A hint here is that the variable "y" represent a point on the line that connects the end points (0,b) and (a,0).

 

The first step to solve this problem is to get the expression of this line.

 

The slope of this line is:   m = (0 - b)/(a - 0) = -b/a

 

Because the point (x,y) is on this line we have:   y - b = m(x - 0)

                                                                       y = (-b/a)x + b

 

Solution: Area of the rectangle = x*y = x*((-b/a)x + b) = (-b/a)x² +bx

 

I hope it helped you.