If the length of a rectangle is represented by #(5x-3)# and the width is represented by #(2x)#, what is the area of the rectangle in terms of #x#? Please show working.

Question

James Atkins · Accepted Answer

For this problem, you ought to remember the formula for area of a rectangle is (length • width)

Let A be area, l be length and w be width. A = (5x - 3)(2x) Use the distributive property --> #10x^2# - 6x The rectangle has an area of #10x^2# - 6x

Evelyn Arboleda · Answer

Area: #10x^2-6x# Area of rectangle #= color(red)("length") xx color(blue)("width")# Area of given triangle #=color(red)((5x-3))xxcolor(blue)((2x))# #color(white)("XXXXXXXXXXX")=(color(red)((5x))xxcolor(blue)((2x)))-(color(red)((3))xxcolor(blue)((2x)))# #color(white)("XXXXXXXXXXX")=10x^2-6x#

Sadie Adams · Answer

undefined To find the area of the rectangle in terms of $ x $, we multiply the length by the width. Given that the length is $ 5x - 3 $ and the width is $ 2x $, the area $ A $ of the rectangle is $ A = (5x - 3) \times (2x) $. To find the product, we distribute $ 2x $ into $ 5x - 3 $.

$ A = 2x \times 5x - 2x \times 3 $

$ A = 10x^2 - 6x $

Therefore, the area of the rectangle in terms of $ x $ is $ 10x^2 - 6x $.