Solution:
Perimeter of quadrilateral = sum of all the four sides
- First side = x + 5
- Second side = x + 8
- Third side = x-2
- Fourth side = x²-3x
- x + 5 + x +8 + 3x-2 + x² - 3x = 46
Combining like terms,
- x² + x + x + 3x - 3x + 5 + 8 -2 = 46
- x² + 5x - 3x + 13 - 2 = 46
- x² + 2x + 11 = 46
- x² +2x = 46 - 11
- x² + 2x = 35
- x² + 2x - 35 = 0
By splitting middle term,
- 7x × (-5x) = 35
- 7x + (-5x) = 2x
- x² + 7x - 5x - 35 = 0
- x (x +7) - 5 (x +7) = 0
- (x -5)(x + 7) = 0
solving for x
x - 5 = 0, x = 5 or
x + 7 = 0, x = - 7
We will take postive value of x, i.e 5.
First side = x + 5
= 5 + 5 = 10
Second side = x + 8
= 5 + 8 = 13
Thrid side = 3x-2
= 3(5) - 2
= 15 - 2 = 13
Fourth side = x²-3x
= 5² - 3(5)
= 25 - 15 = 10