Answer:
10
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 .
- 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 ,
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
- Since sides can't be negative ,
x = 10
<h3>
Hence the required answer is 10.</h3>
Let the first number be = x
Let the second number which is consecutive be = x+1
As given, the product of two consecutive square numbers is 144
Square rooting both sides we get
or 
Neglect the negative value so we get x=3
Hence, one number is 3 and the consecutive number is = 3+1=4
The square of the numbers are 9 and 16.
