Answer:The area of the inner rectangle is 66 cm^2
Step-by-step explanation:
The diagram is that of a rectangle with a certain thickness. The area of the outer rectangle is given as 99cm^2. The length I given as (x + 5) and the width is given as x + 3.
The formula for the area of a rectangle is expressed as length, ×width,w. Therefore,
(x + 5)((x + 3) = 99
x^2 + 3x + 5x + 15 = 99
x^2 + 3x + 5x + 15 - 99 = 0
x^2 + 8x - 84 = 0
x^2 + 14x - 6x - 84 = 0
x(x + 14) - 6(x + 84) = 0
(x + 14)(x - 6) = 0
x + 14 = 0 or x - 6 = 0
x = - 14 or x = 6
x cannot be negative so x = 6 cm
The length of the inner rectangle is 2x - 1 = 2×6 - 1 = 12 - 1 = 11 cm.
The width of inner rectangle is x = 6 cm. The area of the inner rectangle is
11×6 = 66 cm^2
