tell and write the expressions in their square in their square forms
a^2-4a+4 and a^2+4a+4
Answers
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+8
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