Question

$\red{\boxed{\mathfrak\colorbox{grey}{Question}}}$
❑The area of a square is 36 cm².
A Rectangle has the same perimeter as the Square. If the breadth of the rectangle is 4cm , find its Length.
❑If a vehicle covers 180 km in 5 Hours and the ratio of its speed to the speed of another vehicle is
3:2 . What is the speed of the second vehicle?​

Answer 1

$\huge{\underline{\underline{\mathtt{\orange{Given}}}}}$

The area of a square is 36 cm². A rectangle has the same perimeter as the square. If the breadth of the rectangle is 4 cm

$\huge{\underline{\underline{\mathtt{\orange{To\:find}}}}}$

Length of the rectangle

$\huge{\underline{\underline{\mathtt{\orange{Solution}}}}}$

Area of square = 36cm²

(side)² = 36

side = √36 = 6cm

Now,

Perimeter of square

= 4 × side

= 4 × 6 = 24cm

Let the length of rectangle be x

According to the given condition

Rectangle has the same perimeter as the square.

Perimeter of square = perimeter of rectangle

=> 24 = 2(l+b)

=> 24 = 2(x+4)

=> 24/2 = x+4

=> 12 = x+4

=> x = 12-4 = 8cm

$\large{\boxed{\frak{\blue{Required\:length=x=8cm}}}}$

$\huge{\underline{\underline{\mathtt{\orange{Verification}}}}}$

Perimeter of square = 24cm

Perimeter of rectangle

= 2(l+b)

= 2(8+4)

= 2×12

= 24

Rectangle has the same perimeter as the square.

Hence, it is verified

$\huge\underline\frak\red{Note}$

Perimeter of rectangle = 2(l+b)

perimeter of square = 4×side

Area of rectangle = l×b

Area of square = side × side

$\huge\purple{\fbox{\tt{ǫᴜᴇsᴛɪᴏɴ}}}$

If a vehicle covers 180 km in 5 Hours and the ratio of its speed to the speed of another vehicle is

3:2 .

$\huge\blue{\fbox{\tt{ᴛᴏ ғɪɴᴅ}}}$

What is the speed of the second vehicle?

$\huge{\textbf{\textsf{{\color{navy}{A}}{\purple{nsw}}{\pink{er}}{\color{pink}{:}}}}}$

Given

Distance covered by car in 5 hours = 180 km

Hence distance covered by car is 3 hours can be

calculated as below

Distance covered by car in 1 hour = 180/5

= 36 km

Distance covered by car in 3 hours = 36 x 3

= 108 km

... Distance covered by car in 3 hours with the same speed will be 108 km

Answer 2

Questions :-

❑The area of a square is 36 cm². A Rectangle has the same perimeter as the Square. If the breadth of the rectangle is 4cm , find its Length.

❑If a vehicle covers 180 km in 5 Hours and the ratio of its speed to the speed of another vehicle is 3:2 . What is the speed of the second vehicle?

___________________

Solution :-

Solution 1 :-

$\bf{ \underline{ \underline{given \: information : - }}} \\ 1.) \: \: \: \sf{ \red{area} \: of \: square = \red{36 \: {cm}^{2} }} \\ 2.) \: \: \: \sf{ \red{perimeter }\: of \: rectangle = \red{perimeter }\: of \: square} \\ 3.) \: \: \: \sf{ \red{breadth }\: of \: rectangle = \red{4 \: cm}}$

$\underline {\underline{ \bf{to \: find \: : - }}} \\ \sf{ \red{length \: of \: the \: rectangle}}$

Calculation :-

Since area of square is given,

$: \implies \sf{area \: of \: square = \red{side}^{ \red2} }$

$: \sf\implies 36 \: {cm}^{2} = {side}^{2}$

$: \implies \sf side = \sqrt{36} = \sf6 \: cm \\ \sf \therefore \: side \: of \: square = \red{6 \: cm}$

Now calculating the perimeter of square,

$\sf perimeter \: of \: square = 4 \times side$

$\sf : \implies \sf perimeter \: of \: square = 4 \times 6 \: cm$

$\sf : \implies \red{perimeter }\: of \: square = \red{24 \: cm}$

Now, it's given that,

$\sf : \implies{perimeter \: of \: \red{square} = perimeter \: of \: \red{rectangle}}$

$\sf \therefore \red{ perimeter} \: of \: rectangle = \red{24 \: cm}$

Now, since breadth of rectangle is given, length can be found using the formula,

$\boxed{ \sf perimeter \: of \: rectangle = \red{2 \times (length + breadth)}}$

Putting the values calculated above,

$\sf : \implies 24 \: cm = 2 \times (length + 4)$

Equating this equation and finding the length,

$\sf : \implies \frac{24}{2} = length + 4$

$\sf : \implies 12 = length + 4$

$\sf : \implies length = 12 - 4 = 8 \: cm \\ \sf\therefore \: \boxed{\boxed{ \red{ \sf length} = \red{ \sf8 \: cm}}}$

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Solution 2 :-

$\bf \underline{ \underline{given \: information : - }} \\ \sf \red{ distance} \: covered {(vehicle \:1) } = \red{ 180 \:km} \\ \sf \: \red{time} \: taken \: (vehicle \: 1) = \red{ 5 \: hours} \\ \sf \red{ ratio} \: of \: speed \: of \: vehicle \: 1 \: to \: vehicle \: 2 = \red{3 : 2}$

$\bf \underline{\underline{to \: find : - }} \\ \sf \: speed \: of \: vehicle \: 2$

Calculation :-

Finding the speed of vehicle 1 in terms of km/hr,

$\sf speed = \frac{distance}{time}$

$\therefore \sf speed = \frac{180}{5} = 36 \: {kmhr}^{ - 1}$

Let the common factor for the speed of two cars be 'x'

$\sf \therefore 3 : 2 = 3x \: and \: 2x$

Calculating the value of 'x',

$\sf : \implies 3x = 36$

$\sf : \implies x = \frac{36}{3} = \red{ 12}$

$\sf \therefore \: \red{ speed }\: of \: vehicle \: 2 = \red{2x }= \red{2 \times 12} = \red{24 \: {kmhr}^{ - 1} }$

$\boxed{ \boxed{ \sf \: \red{speed \: of \: vehicle \: 2 = {24kmhr}^{ - 1}} }}$

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Final Answers :-

Answer 1)= Length of the Rectangle = 8 cm

Answer 2)= Speed of vehicle 2 = 24 km/hr

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Note :-

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