The diagram shows a square - OCR - GCSE Maths - Question 16 - 2020 - Paper 1
Question 16
The diagram shows a square.
(4x – 10) cm
(11 – 2x) cm
By setting up and solving an equation, show that the perimeter of the square is numerically equal to the are... show full transcript
Worked Solution & Example Answer:The diagram shows a square - OCR - GCSE Maths - Question 16 - 2020 - Paper 1
Step 1
Step 1: Identify the side length
96%
114 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Since the question states that the shape is a square, all sides are equal. We can denote the side length as either (s = (4x - 10) \text{ cm}) or (s = (11 - 2x) \text{ cm}). Therefore, we can set up the equation:
[(4x - 10) = (11 - 2x)]
Step 2
Step 2: Solve for \(x\)
99%
104 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
To solve for (x), we rearrange the equation:
[4x - 10 = 11 - 2x]
Adding (2x) to both sides gives:
[6x - 10 = 11]
Adding (10) to both sides results in:
[6x = 21]
Finally, dividing by (6) yields:
[x = \frac{21}{6} = 3.5]
Step 3
Step 3: Calculate the side length
96%
101 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
Now substituting the value of (x) back into either expression to find the side length:
[s = 4(3.5) - 10 = 14 - 10 = 4\text{ cm}]
or
[s = 11 - 2(3.5) = 11 - 7 = 4\text{ cm}]
Both methods confirm that the side length is 4 cm.
Step 4
Step 4: Calculate the perimeter and area
98%
120 rated
Only available for registered users.
Sign up now to view full answer, or log in if you already have an account!
Answer
The perimeter (P) of a square is given by:
[P = 4s = 4(4) = 16\text{ cm}]
The area (A) of the square is:
[A = s^2 = 4^2 = 16\text{ cm}^2]
Thus, we can see that the perimeter is numerically equal to the area, as both are 16.
