Question

The length of a standard jewel case is 3 cm more than its width. The area of the rectangular top of the case is 304 cm squared. Find the length and width of the jewel case.

Answer 1

width = 16 cm

length = 19 cm

Explanation:

Let the width be x cm.

Given that length is 3 cm more than width then

length = x+3 cm

area of rectangle = 304 square cm. -----1

area of rectangle is given by

area =length * width

substituting from equation 1 and length and width in terms of x we have

304 = x(x+3)

`=> 304 = x^2+3x\\\\=> 304 -304= x^2+3x -304\\=> 0= x^2+3x -304\\=> x^2+3x -304 = 0\\=> x^2+19x - 16x -304 = 0\\=> x(x+19 ) -16(x+19) = 0\\=> (x-16) (x+19 )= 0\\x-16 = 0 \ or \ x+19 = 0\\ x= 16 \or \ x = -19`

As length cannot be negative hence x = 16

Thus width = x = 16 cm

length = x+3 = 16+3 = 19 cm