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

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Marked as Best Answer

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**

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