(60 Points)Be brainliest.....By answering this..I want step by step process..........I want No.38,39,40
Answers
Here is your answers:
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38)
The length is 12 m more than breadth.
Let the breadth be x.
Length is 12 + x
Area is 4 * Perimeter
Area of a rectangle is l b...................(1)
Perimeter is 2 ( l + b ).................(2)
Area = 4 (Perimeter)
From 1 and 2:
==> l b = 4 * 2 ( l + b)
==> l b = 8 ( l +b )
But breadth is x and length is 12 + x
==> x ( 12 + x ) = 8 ( 12 + x + x)
==> 12 x + x ² = 8 ( 12 + 2 x)
==> 12 x + x² = 96 + 16 x
==> x² - 4 x - 96 = 0
==> x² - 12 x + 8 x - 96 = 0
==> x( x - 12 ) + 8(x-12 ) = 0
x =12 or x = 8
Length is 12 + x
==> 12 + 12 or 12 + 8
==> 24 or 20
But if l is 20 then it does not satisfy the condition.
So l must be 24 and b is 12 .
The dimensions are 24 m and 12 m
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39)
Perimeter is 2 ( l + b)
Given Perimeter is 68 m
2 ( l + b) = 68
==> l + b= 34 ...........................(1)
Diagonal = is given 26 m
==> Squaring both sides:
l² + b² = 26 ²
==> l² + b² = 676 .............................(2)
We know that (a+b)² = a² + b² + 2 a b
( l +b)² = 34² [From 1 ]
==> l² + b² + 2 l b = 1156
==> 676 + 2 l b = 1156 [From 2 ]
==> 2 l b = 480
==> lb = 480 / 2
==> l b =240 m²
The area is 240 m²
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40)
Let the side of the square be x.
Length of rectangle is 12 + x
Breadth of rectangle is 8 + x
The area of rectangle is twice of the square.
The area of square is x²
Area of rectangle is ( 12 + x)(8 + x)
==>(12+x)(8+x)=2x²
==> x² + 12 x + 8 x + 96 = 2x²
==> -x² + 20 x + 96 = 0
==> x² -20 x - 96 =0
==> x² - 24 x + 4 x - 96 =0
==> x ( x - 24 ) + 4( x - 24 )=0
==>( x + 4 )(x - 24 )=0
x is either 24 or x is -4
but x cannot be negative.
x is 24
So the perimeter is 4 x
==> 4* 24
==> 96 cm
The area is 96 cm
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Hope it helps you
Answer:
Step-by-step explanation:
Here is your answers:
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38)
The length is 12 m more than breadth.
Let the breadth be x.
Length is 12 + x
Area is 4 * Perimeter
Area of a rectangle is l b...................(1)
Perimeter is 2 ( l + b ).................(2)
Area = 4 (Perimeter)
From 1 and 2:
==> l b = 4 * 2 ( l + b)
==> l b = 8 ( l +b )
But breadth is x and length is 12 + x
==> x ( 12 + x ) = 8 ( 12 + x + x)
==> 12 x + x ² = 8 ( 12 + 2 x)
==> 12 x + x² = 96 + 16 x
==> x² - 4 x - 96 = 0
==> x² - 12 x + 8 x - 96 = 0
==> x( x - 12 ) + 8(x-12 ) = 0
x =12 or x = 8
Length is 12 + x
==> 12 + 12 or 12 + 8
==> 24 or 20
But if l is 20 then it does not satisfy the condition.
So l must be 24 and b is 12 .
The dimensions are 24 m and 12 m
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39)
Perimeter is 2 ( l + b)
Given Perimeter is 68 m
2 ( l + b) = 68
==> l + b= 34 ...........................(1)
Diagonal = is given 26 m
==> Squaring both sides:
l² + b² = 26 ²
==> l² + b² = 676 .............................(2)
We know that (a+b)² = a² + b² + 2 a b
( l +b)² = 34² [From 1 ]
==> l² + b² + 2 l b = 1156
==> 676 + 2 l b = 1156 [From 2 ]
==> 2 l b = 480
==> lb = 480 / 2
==> l b =240 m²
The area is 240 m²
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40)
Let the side of the square be x.
Length of rectangle is 12 + x
Breadth of rectangle is 8 + x
The area of rectangle is twice of the square.
The area of square is x²
Area of rectangle is ( 12 + x)(8 + x)
==>(12+x)(8+x)=2x²
==> x² + 12 x + 8 x + 96 = 2x²
==> -x² + 20 x + 96 = 0
==> x² -20 x - 96 =0
==> x² - 24 x + 4 x - 96 =0
==> x ( x - 24 ) + 4( x - 24 )=0
==>( x + 4 )(x - 24 )=0
x is either 24 or x is -4
but x cannot be negative.
x is 24
So the perimeter is 4 x
==> 4* 24
==> 96 cm
The area is 96 cm
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Hope it helps you