Question

1:the area of a rectangular floor is 32m².if it's breadth is half of its length find its perimeter

2:the perimeter of a square is 12cm
find its length find its area

3:the perimeter of a squared field is 60m. find its area

4: the perimeter of a rectangle is 28 cm and it's length is 8cm.
find its breadth find its area

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Answer 1

Answer:

Step-by-step explanation:

1)  length = x m

breadth = x/2 m

Area of rectangular floor = 32 square m

$length * breadth = 32\\\\x*\dfrac{1}{2}x = 32\\\\\\x^{2}=32*2\\\\\\x^{2} = 64\\\\x=\sqrt{64}=\sqrt{8*8}\\\\x = 8 \ m$

Length = 8 m

Breadth =8/2 = 4 m

Perimeter = 2*(length + breadth) = 2*(8 + 4)

                = 2*12

                = 24 m

2) Perimeter of square = 12 cm

Side of a square = perimeter ÷ 4 = 12 ÷ 4 = 3 cm

Area =side *side = 3*3 = 9 cm²

3) Perimeter of square field = 60 m

Side = Perimeter ÷ 4 = 60 ÷4 = 15 m

Area of square = 15 * 15 = 225 m²

4) Perimeter of rectangle = 28 cm

breadth = (Perimeter ÷ 2) - length

             = (28 ÷2) - 8

             = 14 - 8

Breadth = 6 cm

Area of rectangle = 8 * 6 = 48 cm

Answer 2

$\bold{\huge{\pink{\underline{ Solutions }}}}$

Answer 1 :-

We have,

• The area of rectangular floor is 32 m²
• Breath is half of its length

Therefore,

Let the length of the rectangular field be x

So,

Breath of the rectangular field will be x/2

We know that,

$\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}$

Subsitute the required values,

$\sf{32 = x }{\sf{\times{\dfrac{x}{2}}}}$

$\sf{32 = }{\sf{\dfrac{x^{2}}{2}}}$

$\sf{ 32}\sf{\times{ 2 = x^{2}}}$

$\sf{ 64 = x^{2}}$

$\bold{ x = 8 m}$

Thus, The length of rectanglular field is 8m

Therefore,

Breath of the rectangular field will be

$\sf{=}{\sf{\dfrac{8}{2}}}$

$\bold{ = 4 m }$

Now,

We have to find the perimeter of the given rectangular field

We know that,

Perimeter of the reactangle

$\bold{\blue{ = 2( L + W) }}$

Subsitute the required values in the above formula :-

Perimeter of the rectangular field

$\sf{ = 2( 8 + 4) }$

$\sf{ = 2}{\sf{\times{12}}}$

$\bold{ = 24 m}$

Hence, The perimeter of the rectangular field is 24 m

Answer 2 :-

We have

• The perimeter of square is 12 cm

Let the side of the square be x

We know that,

$\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}$

Subsitute the required values in the above formula :-

$\sf{12 = 4 }{\sf{\times{ x }}}$

$\sf{\dfrac{ 12}{4}}{\sf{ = x }}$

$\bold{ x = 3 cm}$

Thus, The length of the square is 3 cm

Now,

We have to find the area of square

We know that,

$\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}$

Subsitute the required values,

Area of square

$\sf{ = 3 }{\sf{\times{ 3 }}}$

$\sf{ = 9 cm^{2}}$

Hence , The length and area of square is 3cm and 9 cm²

Answer 3 :-

We have

• The perimeter of square feild is 60 m

Let the side of the square feild be x

We know that,

$\bold{\pink{ Perimeter\: of\: square = 4 }}{\bold{\pink{\times{ side}}}}$

Subsitute the required values,

$\sf{60 = 4 }{\sf{\times{ x }}}$

$\sf{\dfrac{ 60}{4}}{\sf{ = x }}$

$\bold{ x = 15 m }$

Thus, The side of the square feild is 15m

Now,

We have to find the area of square

We know that,

$\bold{\red{Area \: of \: square = Side }}{\bold{\red{\times{ Side}}}}$

Subsitute the required values,

Area of square

$\sf{ = 15 }{\sf{\times{ 15 }}}$

$\sf{ = 225 cm^{2}}$

Hence, The area of square feild is 225 cm²

Answer 4 :-

We have,

• The perimeter of rectangle is 28 cm
• The length of rectangle is 8 cm

Let the breath of the rectangle be x

We know that,

$\bold{\blue{Perimeter\:of\: rectangle= 2( L + W) }}$

Subsitute the required values,

$\sf{ 28 = 2( 8 + x) }$

$\sf{ 28 = 16 + 2x }$

$\sf{ 28 - 16 = 2x }$

$\sf{ 12 = 2x }$

$\sf{\dfrac{ 12}{2}}{\sf{ = x }}$

$\bold{ x = 6 cm}$

Thus, The breath of the rectangle is 6 cm

Now,

We have to find the area of rectangle

We know that,

$\bold{\red{Area \: of \: rectangle = length}}{\bold{\red{\times{ Breath}}}}$

Subsitute the required values,

Area of rectangle

$\sf{= 8 }{\sf{\times{6}}}$

$\sf{ = 48 cm^{2}}$

Hence, The breath and area of rectangle is 6cm and 48 cm² .

[ Note :- Kindly refer app for better understanding ]