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 = [tex]294cm^{2}[/tex]
Now, Area of a Rectangle = Length x Width
= m x (m + 7)
⇒ m x (m + 7) = 294
or, [tex]m^{2} + 7m - 294 = 0[/tex]
⇒ [tex]m^{2} + 21m - 14m - 294 = 0[/tex]
or, [tex]m(m+21) -14( m + 21)[/tex]
⇒(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
