Question

B) Then solve for x given that the area of the shaded region is 48 square units. Show all your work

Answer 1

10

Explanation:

Here it's given that the area of the shaded region is 48 u² and we need to find out the value of x .

The given figure is made up of two rectangles where the smaller one is inscribed into the bigger one .

• The area of shaded region will be equal to the difference of the areas of the two rectangles , that is equal to 48 u² .
• The area of rectangle is length × breadth .
• The dimensions of bigger rectangle is (x+3)(x-4) and that of smaller one is 3 × x .

So that ,

`\longrightarrow` ar(bigger) - ar(smaller) = 48

`\longrightarrow` [ (x+3) (x-4)] - 3(x) = 48

`\longrightarrow` [ x² - 4x +3x -12 - 3x ] = 48

`\longrightarrow` x² -4x -12 -48 = 0

`\longrightarrow` x² - 4x - 60 = 0

`\longrightarrow` x² - 10x + 4x - 60 = 0

`\longrightarrow` x( x -10) +4(x -10) = 0

`\longrightarrow` (x +4)(x-10) = 0

`\longrightarrow` x = -4,10

• Since sides can't be negative ,

`\longrightarrow` x = 10

Hence the required answer is 10.