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

`\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{*{ Breath}}}}`

Subsitute the required values,

`\sf{32 = x }{\sf{*{(x)/(2)}}}`

`\sf{32 = }{\sf{(x^(2))/(2)}}`

`\sf{ 32}\sf{*{ 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{(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{*{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{*{ side}}}}`

Subsitute the required values in the above formula :-

`\sf{12 = 4 }{\sf{*{ x }}}`

`\sf{( 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{*{ Side}}}}`

Subsitute the required values,

Area of square

`\sf{ = 3 }{\sf{*{ 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{*{ side}}}}`

Subsitute the required values,

`\sf{60 = 4 }{\sf{*{ x }}}`

`\sf{( 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{*{ Side}}}}`

Subsitute the required values,

Area of square

`\sf{ = 15 }{\sf{*{ 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{( 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{*{ Breath}}}}`

Subsitute the required values,

Area of rectangle

`\sf{= 8 }{\sf{*{6}}}`

`\sf{ = 48 cm^(2)}`

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

[ Note :- Kindly refer app for better understanding ]

Answer 2

Explanation:

1) length = x m

breadth = x/2 m

Area of rectangular floor = 32 square m

`length * breadth = 32\\\\x*(1)/(2)x = 32\\\\\\x^(2)=32*2\\\\\\x^(2) = 64\\\\x=√(64)=√(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