'n Stuk draad wat 6 meter lank is, word in twee stukke gesny - NSC Mathematics - Question 9 - 2017 - Paper 1
Question 9
'n Stuk draad wat 6 meter lank is, word in twee stukke gesny. Een stuk, $x$ meter lank, word gebruik om 'n vierkant ABCD te vorm. Die ander stuk word in 'n U-vorm ge... show full transcript
Worked Solution & Example Answer:'n Stuk draad wat 6 meter lank is, word in twee stukke gesny - NSC Mathematics - Question 9 - 2017 - Paper 1
Step 1
Length of one side of the square
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Answer
The length of one side of the square is given by ( \frac{x}{4} ).
Step 2
Length of the rectangle
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Answer
The remaining length of the wire for forming the rectangle is given by ( 6 - x ). Therefore, the length of the rectangle, denoted as ( l ), can be expressed as follows: [ l = 6 - 5 ] = ( 24 - 5x ) .
Step 3
Calculate the area
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Answer
The total area ( A ) of the shapes formed can be calculated as: [ A = \left( \frac{x}{4} \right)^{2} + \left( 24 - 5x \right) \left( \frac{x}{4} \right) ]. Simplifying this gives: [ A = \frac{24x - 3x^{2}}{32} ].
Step 4
Finding the maximum area
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Answer
To find the maximum area, we take the derivative of the area function ( A ) with respect to ( x ) and set it to zero: [ \frac{dA}{dx} = 24 - 6x = 0 ]. Solving for ( x ) provides ( x = 4 ).
