A carpenter wants to create a rectangular coffin with an area of 52 square feet. He wants the length of the coffin to be 8 feet longer than twice the width. What dimensions should be used for the coffin?

1 Answer
Oct 20, 2017

Length = 14.9544, Breadth = 3.4772

Explanation:

Area of a rectangle = l * b
Area = 52 sqft.

Length l = 2b + 8

#:.l* b = (2b+8)*b = 52 color (white)(aaa) #substituting value of l as b.
#2b^2 + 8b - 52 = 0#
#b = (-8 +-sqrt(8^2 + 4*2*52))/(2*2) = (-8+- sqrt(480))/4#

#b = -2 + sqrt30 = 3.4772 ft color (white)(aaa) #taken only positive value as length cannot be negative.

#l = 2b + 8 = (2 * 3.4772) + 8 = 6.9544 + 8 = 14.9544 ft#

Verification : #Area = l*b = 14.9544 * 3.4772 = 52 sqft