Math, asked by rubitiwary97, 5 months ago

2. Give that the
H.CF of two
numbers is 36 and their produc
is 22176 i determine the L.CM:​

Answers

Answered by mahima757575
1

Step-by-step explanation:

Given

Length of rectangle ⇒ 3x - 4y + 6z

Perimeter of rectangle ⇒ 7x + 8y + 17z

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To Find

The breadth of the rectangle.

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Solution

Perimeter of the given rectangle ⇒ 7x + 8y + 17z

Perimeter of rectangle ⇒ 2 × (Length + Breadth)

Length ⇒ 3x - 4y + 6z

Breadth ⇒ b

Equation to find the breadth ⇒ 2 (3x - 4y + 6z + b) = 7x + 8y + 17z

Let's solve your equation step-by-step

2 (3x - 4y + 6z + b) = 7x + 8y + 17z

Step 1: Open the bracket and substitute the values.

⇒ 2 (3x - 4y + 6z + b) = 7x + 8y + 17z

⇒ 6x - 8y + 12z + 2b = 7x + 8y + 17z

Step 2: Subtract 7x from both sides of the equation.

⇒ 6x - 8y + 12z + 2b - 7x = 7x + 8y + 17z

⇒ -x - 8y + 12z + 2b = 8y + 17z

Step 3: Subtract 8y from both sides of the equation.

⇒ -x - 8y + 12z + 2b - 8y = 8y + 17z - 8y

⇒ -x - 16y + 12z + 2b = 17z

Step 4: Subtract 17z from both sides of the equation.

⇒ -x - 16y + 12z + 2b - 17z = 17z - 17z

⇒ -x - 16y - 5z + 2b = 0

Step 5: Add x + 16y + 5z to both sides of the equation.

⇒ -x - 16y - 5z + 2b + x + 16y + 5z = x + 16y + 5z

⇒ 2b = x + 16y + 5z

Step 6: Divide 2 from both sides of the equation.

⇒ \dfrac{2b}{2} = \dfrac{x+16y+5z}{2}

2

2b

=

2

x+16y+5z

⇒ b= \dfrac{x+16y+5z}{2}b=

2

x+16y+5z

Let's verify the value of the breadth.

⇒ 2(3x-4y+6z +\dfrac{x+16y+5z}{2} ) = 7x + 8y + 17z2(3x−4y+6z+

2

x+16y+5z

)=7x+8y+17z

⇒ 2(3x-4y+6z +(x+16y+5z) \times \dfrac{1}{2} ) = 7x + 8y + 17z2(3x−4y+6z+(x+16y+5z)×

2

1

)=7x+8y+17z

⇒ 2(3x-4y+6z +\dfrac{1}{2} x+8y+\dfrac{5}{2} z ) = 7x + 8y + 17z2(3x−4y+6z+

2

1

x+8y+

2

5

z)=7x+8y+17z

⇒ 2(3x+\dfrac{1}{2} x+8y-4y +\dfrac{5}{2} z +6z) = 7x + 8y + 17z2(3x+

2

1

x+8y−4y+

2

5

z+6z)=7x+8y+17z

⇒ 2(\dfrac{6}{2} x+\dfrac{1}{2} x+8y-4y +\dfrac{5}{2} z +\dfrac{12}{2} z) = 7x + 8y + 17z2(

2

6

x+

2

1

x+8y−4y+

2

5

z+

2

12

z)=7x+8y+17z

⇒ 2(\dfrac{7}{2} x+4y +\dfrac{17}{2} z) = 7x + 8y + 17z2(

2

7

x+4y+

2

17

z)=7x+8y+17z

⇒ 7x + 8y + 17z = 7x + 8y + 17z7x+8y+17z=7x+8y+17z

∴ The value of the breadth of the rectangle is ⇒ \bf \dfrac{x+16y+5z}{2}

2

x+16y+5z

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