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