finding base and height

Question

The area of a parallelogram is given by the formula A=bh.
The area of the parallelogram is 175 sq. units.
Find its base and height if the base is 4x+1 and the height is x+1.

Answer 1

ok...so the area A=(x+1)(4x+1) = 4x^2+5x+1=175.....Subtracting 175 frmo both sides yields...4x^2+5x-174=0.   The factors of 4: ± (1,2,4), and factors of 174: ±(1,2,3,6,29,58,87,174).  Finding the right combination of factors of 4 multiplied by the factors of -174 takes some thought and writing down on paper....but the factors of 4 are 4,1 and of -174 are 29, -6.  

 

(4x+29)(x-6)=0.....

 

So  4x+29=0, so x= -29/4 = -7 1/4   OR  X-6=0, so x=6.  IF WE PLUG -29/4 IN FOR EITHER BASE OR HEIGHT , THEN WE END UP WITH NEGATIVE LENGTHS SO -29/4 IS NOT TO BE USED.....X=6 IS TO BE USED, SO BASE=4X+1=4(6)+1=25, AND HEIGHT=X+1=6+1=7.

 

 

Answer 2

(4x + 1)(x + 1) = 175

 

Can you solve for x and answer?