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20 Here are three similar triangles - OCR - GCSE Maths - Question 20 - 2018 - Paper 1
Question 20
20 Here are three similar triangles. 15 cm 21 cm Work out the value of x. (a) x = (b) The diagram shows two right-angled triangles, OAB and OCD. A ... show full transcript
Worked Solution & Example Answer:20 Here are three similar triangles - OCR - GCSE Maths - Question 20 - 2018 - Paper 1
Step 1
Work out the value of x.
Answer
To find the value of x in the similar triangles, we can use the ratio of corresponding sides.
The sides of the triangles are as follows:
- For the largest triangle: 15 cm (height) and 21 cm (base).
- For the medium triangle: 4 cm (height) and x (base).
- For the smallest triangle: 5 cm (height) and 8 cm (base).
Using the ratio of the sides:
the ratios are:
-
Largest triangle to medium triangle:
Cross-multiplying gives:
Thus:
So, the value of x is 5.6.
Step 2
Work out the length of BD.
Answer
To find the length of BD in triangle OAB and OCD, we can use the right triangle properties and the Pythagorean theorem.
In triangle OCD:
- The lengths given are 4 cm (height) and 7 cm (base).
- To find OD:
Using Pythagoras' theorem:
- Here, we note that OB is 14 cm for triangle OAB.
Thus: Setting OD = 7 cm:
But since we are measuring BD relating to the original dimensions: Since 4 cm is vertical and 7 cm is horizontal, the length of BD is computed to be:
By measuring proportions, based on OAB, we can simplify. Typically, the length of BD is calculated using the scaling ratio derived from OAB's 14 cm to 4 cm. The final value of BD is thus derived directly from the geometry involved.