Answer:
Length = 11 cm and Width = 7 cm.
Step-by-step explanation:
If length of a rectangle is L and the width is W, then perimeter(P) of the rectangle is given by 2(L + W) = 36 cm. {Given}
⇒ L + W = 18 ......(1)
Again, the area(A) of the rectangle is LW = 77 sq. cm. {It is also given}
⇒ [tex]W = \frac{77}{L}[/tex] ......... (2)
Now, from equation (1), we get.
[tex]L + \frac{77}{L}= 18[/tex]
⇒[tex]L^{2}-18L +77 =0[/tex]
⇒ (L - 7)(L - 11) = 0
⇒ L = 7 or L = 11
Now, since L > W so, we chose L = 11 cm and W = 7 cm. (Answer)
