Question

The length of a standard jewel case is 7cm more than its width. The area of the rectangular top of the case is 294 cm^2. Find the length and width of the jewel case.

Answer 1

Answer:

Length = 21 cm

Width = 14 cm

Step-by-step explanation:

Let the width of the jewel case = m cm

So, the length of the case = (m + 7) cm

Area of the case = $294cm^{2}$

Now, Area of a Rectangle = Length x Width

=   m x (m + 7)

⇒  m x (m + 7) = 294

or, $m^{2} + 7m - 294 = 0$

⇒  $m^{2} + 21m - 14m - 294 = 0$

or, $m(m+21) -14( m + 21)$

⇒(m + 21)(m -14) = 0

Hence, either (m + 21) = 0  ⇒ m  = -21

or, (m -14) = 0⇒ m = 14

Since, m is the width of a case, so it can not be negative

Hence the width of the jewel case = m = 14 cm

And the length of the case = (m + 7) = 14 + 7 = 21 cm