Question

A path 1 m wide is built along the border and inside a square garden of side 30 m. Find the cost of planting grass in the remaining portion of the garden at the rate of Rs 50 per sq m *
5 points
Rs. 31,360
Rs. 35,630
Rs. 37,360
Rs. 39,200

Answer 1

$\\\;\underbrace{\underline{\sf{Understanding\;the\;Question\;:-}}}$

Here the concept of Areas of Square has been used. We see that we are given the dimension of the square and also width of path. This means the area to be grassed will also be a square only since path is uniform. So first we need to find the dimension of the square area to be grassed. This can be found out by subtracting twice the width of road from each side of garden. Thus we can find side and area to be grassed and then total cost.

Let's do it !!

_________________________________________________

★ Equations Used :-

$\\\;\boxed{\sf{Area\;of\;Square\;=\;\bf{(Side)^{2}}}}$

$\\\;\boxed{\sf{Total\;cost\;of\;grassing\;=\;\bf{Rate_{(in\;per\;m^{2})}\;\times\;Area\;to\;grassed}}}$

_________________________________________________

★ Solution :-

Given,

» Side of the garden = 30 m

» Width of Road = 1 m

» Rate of grassing per m² = Rs. 50

_________________________________________________

~ For the Area to be Grassed :-

Since, the remaining portion is square. Then, its side will be -

✒ Side of remaining portion = 30 - 2(width of road)

✒ Side of remaining portion = 30 - 2(1)

✒ Side of remaining portion = 30 - 2

✒ Side of remaining portion = 28 cm

Now area of square is given as -

$\\\;\;\;\sf{:\rightarrow\;\;Area\;of\;Square\;=\;\bf{(Side)^{2}}}$

$\\\;\;\;\sf{:\rightarrow\;\;Area\;of\;Square_{(to\;be\;grassed)}\;=\;\bf{(28)^{2}}}$

$\\\;\;\;\sf{:\rightarrow\;\;Area\;of\;Square_{(to\;be\;grassed)}\;=\;\bf{(28)^{2}}}$

$\\\;\;\;\bf{:\rightarrow\;\;Area\;of\;Square_{(to\;be\;grassed)}\;=\;\bf{784\;\;m^{2}}}$

$\\\;\underline{\boxed{\tt{Area\;\;of\;\;Remaining\;\;Portion\;=\;\bf{784\;\;m^{2}}}}}$

_________________________________________________

~ For Total Cost of Grassing the remaining portion ::

We already know the rate and area to be grassed. Then,

$\\\;\;\;\sf{:\mapsto\;\;Total\;cost\;of\;grassing\;=\;\bf{Rate_{(in\;per\;m^{2})}\;\times\;Area\;to\;grassed}}$

$\\\;\;\;\sf{:\mapsto\;\;Total\;cost\;of\;grassing\;=\;\bf{50\;\times\;784}}$

$\\\;\;\;\bf{:\mapsto\;\;Total\;cost\;of\;grassing\;=\;\bf{Rs.\;\;39,200}}$

Hence, option d.) Rs. 39,200 is correct.

$\\\;\underline{\underline{\rm{Thus,\;total\;cost\;of\;grassing\;is\;\;\boxed{\bf{Rs.\;\;39,200}}}}}$

_________________________________________________

★ More to know :-

Now let us find the Area of Path. This can be given as,

$\\\;\tt{\Rightarrow\;\;Area\;\;of\;\;Path\;=\;Area\;\;of\;\;Garden\;-\;Area\;\;to\;\;be\;\;grassed}$

$\\\;\tt{\Rightarrow\;\;Area\;\;of\;\;Path\;=\;(Side)^{2}\;-\;784}$

$\\\;\tt{\Rightarrow\;\;Area\;\;of\;\;Path\;=\;(30)^{2}\;-\;784}$

$\\\;\tt{\Rightarrow\;\;Area\;\;of\;\;Path\;=\;900\;-\;784}$

$\\\;\bf{\Rightarrow\;\;Area\;\;of\;\;Path\;=\;116\;\;m^{2}}$

_________________________________________________

★ Extra Formulas :-

$\\\;\sf{\leadsto\;\;Area\;of\;Rectangle\;=\;Length\;\times\;Breadth}$

$\\\;\sf{\leadsto\;\;Area\;of\;Circle\;=\;\pi r^{2}}$

$\\\;\sf{\leadsto\;\;Area\;of\;Triangle\;=\;\dfrac{1}{2}\;\times\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Parallelogram\;=\;Base\;\times\;Height}$

$\\\;\sf{\leadsto\;\;Area\;of\;Rhombus\;=\;\dfrac{1}{2}\;\times\;(Sum\;of\;||^{el}\;sides)\;\times\;Height}$

Answer 2

$\large\purple{\boxed{\sf{Answer⤵}}}$

✏ Rs.39,200

Given,

Side of Garden = 30m

Width of Road = 1m

Rate of grassing per m² = Rs.50

To find,

Cost of planting grass in remaining portion

Solution,

Side of remaining portion = 30 - 2(width of road)

Side of remaining portion = 30 - 2(1)

Side of remaining portion = 30 - 2

$\large\pink{\boxed{\sf{Side=28m}}}$

Area of square,

$\large\sf area \: of \: square = {side}^{2}$

$\large\sf area \: of \: square = ({28})^{2}$

$\large\orange{\boxed{\sf{Area\: of\: remaining\: portion=784m²}}}$

Cost of Grassing :-

Total cost of grassing = Rate(per m²) × Area to be grassed

Total cost of grassing = 50 × 784m²

$\large\red{\boxed{\sf{Total\: cost=Rs.39,200}}}$