Question

. Length and breadth of a rectangular plate are
measured to be L =
(4.0 +- 0.2) m and
B = (2.0 +- 0.1) m respectively, then perimeter of
the plate is
[NCERT Pg. 26]
(1) 12.0 +- 0.3 m (2) 12.0 +- 0.6 m
(3) 6.0 +- 0.3 m
(4) 6.0 +- 0.2 m​

Answer 1

Answer:

(2) 12.0 ± 0.6 m

Explanation:

L= 4.0 m, ΔL= ±0.2 m      and        B = 2.0 m , ΔB = ±0.1 m

We know that,                                                                                                                               ⇒           Perimeter(P)= 2(L+B)                                                                                                   So,                                                                                                                                                                 ⇒                   P = 2(4.0+2.0)  

⇒                   P = 2(6.0)

⇒                   P = 12.0 m

Now, finding the error in permiter i.e. ΔP

⇒                   ΔP = 2(ΔL + ΔB)

⇒                   ΔP = 2(0.2 + 0.1)

⇒                   ΔP = 2(0.3)

⇒                   ΔP = 0.6 m

So, the perimeter of the rectangular plate = (P±ΔP)

                                                                        = (12.0 ± 0.6) m

Answer 2

Given,

Dimensions of a rectangular plate;

Length = L = (4.0 +- 0.2) m

Breadth = B = (2.0 +- 0.1) m

To find,

The perimeter of the rectangular plate.

Solution,

We can simply solve this mathematical problem using the following process:

Mathematically,

the perimeter of a rectangle

= 2 x (length + breadth)

Also,

If two or more values are added or multiplied, then their respective errors also get added or multiplied, respectively.

Now,

the perimeter of the rectangular plate

= 2 x (length + breadth)

= 2 x (L + B)

= 2 x {(4.0 +- 0.2) m + (2.0 +- 0.1) m}

= 2 x {(6.0 +- 0.3) m}

= 12.0 +- 0.6 meters

Hence, the total perimeter of the rectangular plate is equal to 12.0 +- 0.6 meters. (Option-2)