The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 4 - 2019 - Paper 1
Question 4
The diagram shows two rectangles, A and B.
Rectangle A has a width of 25 cm and a height of 12 cm.
The width of rectangle B is three times the height of rectangle B... show full transcript
Worked Solution & Example Answer:The diagram shows two rectangles, A and B - OCR - GCSE Maths - Question 4 - 2019 - Paper 1
Step 1
Find the area of rectangle A
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Answer
The area of rectangle A can be calculated using the formula:
extArea=extwidthimesextheight
For rectangle A:
extAreaA=25extcmimes12extcm=300extcm2
Step 2
Set up the equation for area of rectangle B
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Answer
Let the height of rectangle B be denoted as x. Then the width of rectangle B is:
extwidthB=3x
The area of rectangle B is:
extAreaB=extwidthBimesextheightB=3ximesx=3x2
Step 3
Equate the areas to find x
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Answer
Since the area of rectangle A is equal to the area of rectangle B, we can set their areas equal to each other:
300=3x2
Dividing both sides by 3 gives:
100=x2
Taking the square root gives:
x=10extcm
Step 4
Calculate the width of rectangle B
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Substituting the value of x back into the width equation:
extwidthB=3x=3imes10=30extcm
Step 5
Find the perimeter of rectangle B
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Answer
The perimeter P of rectangle B can be calculated using the formula:
