Answer:
The length of the case is 24 cm and its width is 17cm.
Step-by-step explanation:
The Length of a standard jewel case is 7cm more than its width.
Let the length be represented by L and the width be represented by W, this means that:
L = 7 + W
The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:
A = L * W
Since L = 7 + W:
A = (7 + W) * W = 7W + W²
The area is 408 cm², hence:
408 = 7W + W²
Solving this as a quadratic equation:
=> W² + 7W - 408 = 0
W² + 24W - 17W - 408 = 0
W(W + 24) - 17(W + 24) = 0
(W - 17) (W + 24) = 0
=> W = 17cm or -24 cm
Since width cannot be negative, the width of the case is 17 cm.
Hence, the length, L, is:
L = 7 + 17 = 24cm.
The length of the case is 24 cm and its width is 17cm.
