Question

pls help me of this question​

Answer 1

First Question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Cost\:of\:fencing=320\:rupees}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given :}} \\ \tt: \implies Area \: of \: square = 400 { \: m}^{2} \\ \\ \green{\underline \bold{Given :}} \\ \tt: \implies Cost \: of \: fencing \: garden =?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: garden = {side}^{2} \\ \\ \tt: \implies 400 = {side}^{2} \\ \\ \tt: \implies side = \sqrt{400} \\ \\ \green{\tt: \implies side = 20 \: m} \\ \\ \bold{For \: Perimeter : } \\ \tt: \implies Perimeter \: of \: garden = 4 \times side \\ \\ \tt: \implies Perimeter \: of \: garden =4 \times 20 \\ \\ \green{\tt: \implies Perimeter \: of \: garden =80 \: m} \\ \\ \bold{For \: cost \: of \: fencing \: ground : } \\ \tt: \implies Cost\: of \:fencing = 4 \times 80 \\ \\ \green{\tt: \implies Cost\: of \:fencing =320 \: rupees}$

Second Question :

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Increase\%\:area=21\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline \bold{Given : }} \\ \tt: \implies Increase \: side\% = 10\% \\ \\ \red{\underline \bold{To \: Find: }} \\ \tt: \implies Increase\%\:area =?$

• According to given question :

$\tt \circ \: Let \: side \: of \: square \: be \: x \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Area \: of \: square = {side}^{2} \\ \\ \tt: \implies Area \: of \: square = {x}^{2} - - - - - (1) \\ \\ \tt \circ \: New \: side = x + 10\% \: of \: x = x + 0.1x = 1.1x \\ \\ \bold{For \: New \: Area : } \\ \tt: \implies New \: Area \: of \: square = {side}^{2} \\ \\ \tt: \implies New \: Area \: of \: square = {(1.1x)}^{2} \\ \\ \tt: \implies New \: Area \: of \: square = 1.21 {x}^{2} - - - - - (2) \\ \\ \bold{For \: increase \% \: area : } \\ \tt: \implies Increase\% \: area = \frac{New \: Area - Actual \: Area}{Actual \: Area} \times 100 \\ \\ \tt: \implies Increase\% \: Area = \frac{1.21 {x}^{2} - {x}^{2} }{ {x}^{2} } \times 100 \\ \\ \tt: \implies Increase\% \: Area = \frac{0.21 {x}^{2} }{ {x}^{2} } \times 100 \\ \\ \tt: \implies Increase\% \: Area =0.21\times 100 \\ \\ \green{\tt: \implies Increase\% \: Area =21\%}$

Answer 2

Questions -

1. The area of a square garden is 400 square metres .

What is the cost of fencing the garden at a rate of Rs. 4 per metre ?

2. If the length of each side of the square is increased by 10% , than what will be the percentage of increase in area ?

Solution -

• Part 1

In the above Question , we have the following information -

The area of a square garden is 400 square metres .

We have to find the cost of fencing the garden at a rate of Rs. 4 per metre .

Let the length of the edge of the square garden be X metres .

Area of the square garden = 400 square metres

=> x^2 = 400

=> x = 20 m

So, the side of the square garden is 20 m.

Perimeter of the garden -

=> 4 × Side

=> 80 metres .

Cost of fencing the garden at a rate of Rs. 4 per metre -

=> Rs. 320 .... A 1

• Part 2

Let the innitial length of the square be l metres .

Now, this is increased by 10 %

Hence ,

New length of side of the square is 1.1 m.

Area of square

=> [ Length ]^2

=> 1.21 l^2

Therefore , Increase in area = 0.21 L^2 = 21%