A piece of cardboard in the shape of a parallelogram is twisted to form the tube for a roll of paper towels. The parallelogram has an area of 60 square inches. If its height h is 7 inches more than the length of the base b, what is the length of the base? (Hint: The formula for the area of a parallelogram is A = bh in

base= 5 in

height  = 12 in

Step-by-step explanation:

Area = base x height

Base = b

Height = b+7

So:

60= b ( b+7)

60 = b^2 +7b

0 = b^2 +7b -60

a= 1 ; b=7 ; c=-60

For: ax2+ bx + c  

x =[ -b ± √b²-4ac] /2a  

Replacing with the values given:  

x =[ -7 ± √(7)²-4(1)-60] /2(1)  

x = [ -7 ± √49 +240] /2  

x = [ -7 ± √289] /2  

x = [ -7 ± 17] /2  

Positive:  

x = [ -7 +17] /2 = 5

So:  

b= 5 in ( base)

Height = b+7 = 5+7 = 12 in

Feel free to ask for more if needed or if you did not understand something.  

< coa = 150 ( given)

as ba and bc are tangents

so oc and oa is perpendicular to cb and ab respectively because in circle normal passes through centre

so in quadrilateral oabc

< coa + < oab + < ocb + < abc = 360

150 +90+90 + < abc = 360

330 + < abc = 360

< abc = 360 -330 = 30

so < abc = 30

⭐dhruv⭐