Question

The figure above represents an L- shaped garden. What is the value of k ?
(1) The area of the garden is 189 square feet.
(2) The perimeter of the garden is 60 feet.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is A Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

R.E.F image

Area $=k\times (15-k)+k\times 15$

$189=k\times 15-k^2+k\times 15$

$\Rightarrow k^2-30k+189=0$

$k=21,9$

Perimeter $=9+15+15+9+21+21$

$=60ft$

$\therefore$ Alone is sufficient