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

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Step-by-step 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 .

So that ,

ar(bigger) - ar(smaller) = 48

[ (x+3) (x-4)] - 3(x) = 48

[ x² - 4x +3x -12 - 3x ] = 48

x² -4x -12 -48 = 0

x² - 4x - 60 = 0

x² - 10x + 4x - 60 = 0

x( x -10) +4(x -10) = 0

(x +4)(x-10) = 0

x = -4,10

x = 10

25/4

step-by-step explanation:

call segment cd's length x. because dc and ab are parallel, angle acd and cab, so triangles adc and abc are similar and we can set up the equation x / ac = ac / ab, or x / 5 = 5 / 4 and x = 25/4.

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