Math Problem Statement
Solution
Let's go through the mathematical questions visible in the image and break them down:
Part (a)
"Complete the statement."
The problem shows two triangles: triangle and triangle . Since , and the triangles share angle , by AA (Angle-Angle) similarity criterion, we can say:
Answer:
- Triangle is similar to triangle .
Part (b)
"Work out the length of ."
We are given that and that the lengths are:
Using the similarity of triangles and , we can set up the proportion:
Substitute the known values:
Simplifying the equation:
Multiply both sides by 8 to find :
Answer:
Part (c)
"The area of triangle is 26.906 cm². Use this value to find the area of triangle ."
Since the triangles and are similar, the ratio of their areas is proportional to the square of the ratio of their corresponding sides.
Substitute the known values:
Simplify:
Multiply both sides by 26.906 to find the area of :
Answer:
- Area of triangle = 6.73 cm² (rounded to 2 decimal places).
Do you want further details on any of these steps?
Here are some questions you might find useful:
- How do you apply the AA similarity criterion in triangles?
- Can you explain the proportionality rule for corresponding sides in similar triangles?
- How do you compute the area ratio for similar triangles?
- What other methods could be used to calculate the length of ?
- What is the geometric meaning behind the similarity of these triangles?
Tip: When working with similar triangles, always check if you can set up proportional relationships between corresponding sides for easy calculations.
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Math Problem Analysis
Mathematical Concepts
Geometry
Triangle Similarity
Proportions
Area of Triangles
Formulas
Proportionality: (AB/CD) = (BX/CX)
Area ratio of similar triangles: (Area of ABX / Area of DCX) = (AB/CD)^2
Theorems
AA Similarity Criterion
Proportionality in Similar Triangles
Suitable Grade Level
Grades 9-11
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