What is the area of rectangle B?

Question

Right triangle A has base b, height h, and area x. Rectangle B has length 2b and width 2h. What is the area of rectangle B in terms of x?

a) 2x

b) 4x

c) 6x

d) 7x

e) 8x

Answer 1

Given:

     Right triangle A:     base = b     ,      height = h     , and     Area = x

     Recall that the area (A) of a triangle is given be the following formula:  

                                 A = (1/2)bh

     Thus, since we are given that the area of triangle A is equal to x, then

                                (1/2)bh = x

     Rectangle B:     length = l = 2b     and      width = w = 2h

     Recall that the area (A) of a rectangle is given by the following formula:  

                                             A = lw

     Thus, the area (A) of rectangle be is as follows:

                                          A = 2b·2h

                                          A = 2·2(bh)

                                          A = 4(bh)

From the area of triangle A, we can solve for bh then substitute this expression in terms of x into the formula of the area of rectangle B above:

    area of triangle A:     (1/2)bh = x      multiply both sides of equation by 2 to solve for bh

                                   2·(1/2)bh = 2·x

                                   bh = 2x

   area of rectangle B:     A = 4(bh)     given bh=2x, replace bh in this equation with 2x

                                     A = 4(2x)

                                     A = 8x

Thus, the area of rectangle B in terms of x is 8x

Answer 2

Hey Sun! Rect bh is two tri bh ... rect 2b: double again ... rect 2b2h: double a third time => 2,4,8 => 8x :)