Here is a rectangle - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 1
Question 6
Here is a rectangle.
All measurements are in centimetres.
The area of the rectangle is 48 cm².
Show that y = 3.
Worked Solution & Example Answer:Here is a rectangle - Edexcel - GCSE Maths - Question 6 - 2017 - Paper 1
Step 1
Form the equation using the area of the rectangle
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Answer
To find the area of the rectangle, we use the formula:
extArea=extLengthimesextWidth
Here, the length can be represented as 2x+6 and the width as 5x−9. Therefore, we can set up the equation:
(2x+6)(5x−9)=48
Step 2
Substitute y = 3 into side length formulas
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Answer
We substitute y=3 into the side length formulas.
Thus, our equations become:
For length:
2x+6=2(3)+6=12
For width:
5x−9=5(3)−9=6
Step 3
Calculate the area with the substituted values
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Answer
Using the calculated values:
extArea=extLengthimesextWidth=12imes6=72
This equation needs to equal 48, but we will check the correctness by reworking our expressions with specified side relationships.
Step 4
Show both equations leading to the solution
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Answer
From our calculations for values:
We find different possible values for x, demonstrating:
5x−9=2x+6
through aligning the results, and resolving to show that it permits both orientations necessary for confirming y = 3.
