The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area areA- 10 cm and 40 cmB- 20 cm and 30 cmC- 15 cm and 35 cmD- 25 cm and 25 cm

The correct option is D 25 cm and 25 cm2x+2y=100 ⇒ x +y =50 ....(i) Let area of rectangle is A; ∴ A =xy ⇒ y =A/x Put in (i), we have x+A/x=50 ⇒ A=50 x x^2 ⇒d ...

You visited us 9 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Local Maxima

The adjacent ...

Question

The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are

10 cm and 40 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

20 cm and 30 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

25 cm and 25 cm

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

15 cm and 35 cm

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 25 cm and 25 cm
$2 x + 2 y = 100 \Rightarrow x + y = 50 . . . . (i)$
Let area of rectangle is A; $∴ A = x y \Rightarrow y = \frac{A}{x}$
Put in (i), we have $x + \frac{A}{x} = 50 \Rightarrow A = 50 x - x^{2}$
$\Rightarrow \frac{d A}{d x} = 50 - 2 x$
For maximum area $\frac{d A}{d x} = 0$
$∴ 50 - 2 x = 0 \Rightarrow x = 25$ and y =25
Hence adjacent sides are 25 and 25 cm.

Suggest Corrections

Similar questions

Q. The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are

Q. What is the perimeter of a rectangle with length 10 cm and breadth 5 cm?

Q. Diagonal of a rectangle is

25 c m

and length is

20 c m

. Find the area of the rectangle?

In the given figure, a circle touches the side BC of Δ A B C at P. AB and AC are two tangents drawn from a point A outside the circle. If AQ = 15 cm, find the perimeter of Δ A B C .

Q. Find the perimeter of a rectangle whose area is 600 cm² and breadth is 25 cm.

Join BYJU'S Learning Program

The adjacent sides of a rectangle with given perimeter as 100 cm and enclosing maximum area are

The correct option is C 25 cm and 25 cm2x+2y=100⇒x+y=50....(i) Let area of rectangle is A; ∴A=xy⇒y=Ax Put in (i), we have x+Ax=50⇒A=50x−x2 ⇒dAdx=50−2x For maximum area dAdx=0 ∴50−2x=0⇒x=25 and y =25 Hence adjacent sides are 25 and 25 cm.