Question

The length of the rectangle below is (2x + 8) cm and its width is (2x + 12) cm

(i) Given that the area of the rectangle is 140 cm2, determine the value of x. (3 points)


(ii) Hence, State the dimensions of the rectangle, in centimeters. (2 points)

Answer 1

Answer:

(i)  x = 1

(ii)  length is 10cm and width is 14cm

Step-by-step explanation:

if you multiply (2x+8) by (2x+12) you get 4x² + 40x + 96

you can set that product equal the area of 140

4x² + 40x + 96 = 140

4x² + 40x = 44

4x² + 40x - 44 = 0

4(x+11)(x-1) = 0

x equals -11 but also 1; however, we can't have a negative length so we disregard -11 and x = 1

dimensions:  2(1)+8 = 10 and 2(1)+12 = 14