Question

Someone help me please, I’m really stuck and I don’t want to fail the test

Answer 1

11 - y = 8 - x--->y - 11 = x - 8 = y = x + 3

42/y = 27/x--->14/(x + 3) = 9/x

14x = 9(x + 3)

14x = 9x + 27

5x = 27

x = 5.4, y = 8.4

Area of shaded rectangle = (27/5.4)(8 - 5.4)

= 5(2.6) = 13 in²

Answer 2

`\text{Let the length of the shaded rectangle be x and width be y.}\\\text{Then from the figure,}\\\mathrm{x(11-y)=42.......(1)}\\\mathrm{x(8-y)=27.......(2)}\\\text{Dividing equation (1) from equation (2),}\\\mathrm{(11-y)/(8-y)}=(42)/(27)\\\\\text{or, }\mathrm{297-27y=336-42y}\\\text{or, }\mathrm{15y=39}\\\text{or, }\mathrm{y=2.6 inch}`

`\text{Equation (2) becomes:}\\\mathrm{x(8-2.6)=27}\\\text{or, }\mathrm{5.4x=27}\\\mathrm{or,\ x=5inch}`

`\text{Now,}\\\text{Area of shaded region = xy = 5(2.6) = 13}\text{in}^2`

Equation (1) and (2) were obtained by using the formula:

Area of rectangle = length x width