There is a rectangle with width #4x# and height #(7/3)x#. What is the area of the rectangle when #x = 6#?

Question

Aaliyah Anderson · Accepted Answer

The Area of the rectangle is #A = 336#.

The formula for rectangle area is #A = l * w#. This means that the Area of the rectangle is equivalent to the width and length (or height) of the rectangle. Since we already know that the width is #4x#, and the height is #7/3 x#, we can plug these into the formula. Our formula now looks like #A = 4x * 7/3 x#. We also know that #x=6#. Plugging in #6#, for our #x# in the equation, we get #A= 4(6) * 7/3 (6/1)#. I have put our #6# into fraction form since that is how we multiply fractions, numerator times numerator, and denominator times denominator. This leaves us with #A = 24 * 42/3#. We can divide #42 -: 3# to get our decimal value, which comes out to be #14#. Now all that is left to do is to multiply #24 * 14# to get our area. #A = 24 * 14 => A = 336#

Caroline Aucoin · Answer

undefined To find the area of the rectangle when x = 6, plug in the value of x into the formula for the area of a rectangle:

Area = width * height

Given width = 4x and height = (7/3)x:

Area = (4x) * ((7/3)x)

Now, substitute x = 6 into the expression:

Area = (4 * 6) * ((7/3) * 6)

Area = 24 * (14)

Area = 336 square units.