Question

The perimeter of a rectangle is 36 cm and it’s area is 77 sq cm. Find the dimensions of the rectangle

Answer 1

Length = 11 cm and Width = 7 cm.

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}

⇒
`W = (77)/(L)` ......... (2)

Now, from equation (1), we get.

`L + (77)/(L)= 18`

⇒
`L^(2)-18L +77 =0`

⇒ (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)