Question

The length of a rectangle is 10 centimeters less than its width. What are the dimensions of the rectangle if its area is 171 square​ centimeters?

Answer 1

Explanation:

let the width = y

the length =y-10

area of rectangle=length ×breadth

171 =y-10×y

171=y^2-10y

it turns into quadratic equation

y^2-10y+171=0

cant be solved by factorization therefore use general formula

y=-b+or-√(b^2-4ab)/2a

a=1 (coefficient of y^2) ,b=-10 , c=171

y=--10+or-√{10^2-4(1)(10)}\2(1)

y=10+or-√{100-40}\2

y=10+or-√60/2

y=10+or-(7.74/2)

y=10+3.87

y=13.87cm

OR

y=10-3.87

y=6.13cm

if y=13.87 then width is 13.87&length is 13.87-10

=3.87

OR

if y=6.13 then width is 6.13&length is 6.13-10=-3.87