Question

A villager Dashrath has a rectangular Garden. The length of the garden is 2
m more than its breadth. If the area of the garden is 48m2. He wants to cover
the garden with fence. If the cost of fence is Rs.20 per metres.
i) Form the expression?
ii) Factorise expression?
iii) Find the dimension of the garden?
iv) Find the expenditure of the fence?​

Answer 1

Answer:

Let the length and breadth of the rectangular plot be 11x and 4x respectively.

\therefore∴ Perimeter of the plot = \frac{Total\ Cost}{Cost\ of\ 1\ meter\ }=\frac{75000}{100}=750\ m

Cost of 1 meter

Total Cost

=

100

75000

=750 m

We know that Perimeter of rectangle = 2 (length + breadth)

Therefore, according to the question,

750=2\left(11x+4x\right)750=2(11x+4x)

\Rightarrow750=2\times15x⇒750=2×15x

\Rightarrow750=30x⇒750=30x

\Rightarrow x=\frac{750}{30}=25⇒x=

30

750

=25

Hence, length of rectangular plot = 11 x 25 = 275 m

And breadth of rectangular plot = 4 x 25 = 100 m

Answer 2

Step-by-step explanation:

Let the breadth of the garden be $a$ m

Then its length is $(a+2)$ m

Given, its area = $48\:m^{2}$

$\Rightarrow a(a+2)=48$

$\Rightarrow a^{2}+2a-48=0$

$\Rightarrow (a+8)(a-6)=0$

This gives $a=-8$ or $a=6$

Since length cannot be negative, $a=6$

So breadth is 6 m and length is 8 m

The perimeter of the garden is

$=2(6+8)$ m

$=2\times 8$ m

$=14$ m

Thus the cost to make the complete fence with Rs. 20 per metre is Rs. (14 × 20) = Rs. 280.

Answers:

i) expression $\to a^{2}+2a-48$

ii) factorization $\to (a+8)(a-6)$

iii) dimensions $\to 6\:m,\:8\:m$

iv) expenditure of the fence $\to Rs.\:280$