please help me with this question
Answers
a)
i) area of rectangle = length × breadth
(in the figure it is given)
= ( x+4)×4x
= 4x²+16x cm²
ii) Total area
= area of rectangle R + area of rectangle Q
we have find the area of rectangle R now we will find area of rectangle Q
area= length × breadth
= ( x+2 ) × ( x+12 )
= x ( x+12) + 2 ( x +12)
= x² + 12x + 2x + 24
= x² + 14x +24
Now we will add area of fig. R and fig. Q
= 4x² + 16x + x² +14x + 24
= 5x² + 30x +24
so we find total area =5x² + 30x +24 cm²
hence proved
b)
Total area is given i.e. 64cm²
Total area = 5x² + 30x +24
Now we get,
5x² + 30x +24 = 64
Solving for variable 'x'.
Reorder the terms:
24 + -64 + 30x + 5x2 = 64 + -64
Combine like terms: 24 + -64 = -40
-40 + 30x + 5x2 = 64 + -64
Combine like terms: 64 + -64 = 0
-40 + 30x + 5x2 = 0
Factor out the Greatest Common Factor (GCF), '5'.
5(-8 + 6x + x2) = 0
Ignore the factor 5.
Subproblem 1
Set the factor '(-8 + 6x + x2)' equal to zero and attempt to solve:
Simplifying
-8 + 6x + x2 = 0
Solving
-8 + 6x + x2 = 0
Begin completing the square.
Move the constant term to the right:
Add '8' to each side of the equation.
-8 + 6x + 8 + x2 = 0 + 8
Reorder the terms:
-8 + 8 + 6x + x2 = 0 + 8
Combine like terms: -8 + 8 = 0
0 + 6x + x2 = 0 + 8
6x + x2 = 0 + 8
Combine like terms: 0 + 8 = 8
6x + x2 = 8
The x term is 6x. Take half its coefficient (3).
Square it (9) and add it to both sides.
Add '9' to each side of the equation.
6x + 9 + x2 = 8 + 9
Reorder the terms:
9 + 6x + x2 = 8 + 9
Combine like terms: 8 + 9 = 17
9 + 6x + x2 = 17
Factor a perfect square on the left side:
(x + 3)(x + 3) = 17
Calculate the square root of the right side: 4.123105626
Break this problem into two subproblems by setting
(x + 3) equal to 4.123105626 and -4.123
Hope it helps
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