The diagram consists of three mathematically similar shapes - OCR - GCSE Maths - Question 17 - 2018 - Paper 5
Question 17
The diagram consists of three mathematically similar shapes.
The heights of the shapes are in the ratio 1 : 4 : 5.
Find the ratio
total shaded area : total unshade... show full transcript
Worked Solution & Example Answer:The diagram consists of three mathematically similar shapes - OCR - GCSE Maths - Question 17 - 2018 - Paper 5
Step 1
total shaded area
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Answer
Let the heights of the shapes be represented as 1h, 4h, and 5h respectively.
The area of similar shapes relates to the square of their heights. Therefore:
The area of the first shape is proportional to \((1h)^2 = 1h^2).
The area of the second shape is proportional to \((4h)^2 = 16h^2).
The area of the third shape is proportional to \((5h)^2 = 25h^2).
Thus, the total area of all three shapes is:
1h2+16h2+25h2=42h2.
Step 2
total unshaded area
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Answer
The shaded area consists of the combined areas of the first two shapes:
1h2+16h2=17h2.
Thus, the unshaded area is the area of the third shape alone:
25h2.
Step 3
final ratio
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Answer
Now, we can find the ratio of the total shaded area to the total unshaded area:
frac17h225h2=frac1725.
In its simplest form, the ratio of total shaded area to total unshaded area is:
