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The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger △ABC be 36 cm, then the longest side of the smaller △DEF is:
- a)27 cm
- b)26 cm
- c)29 cm
- d)30 cm
Correct answer is option 'A'. Can you explain this answer?
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The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
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The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
What we need to know here is,
Supplement angles means. Sum of both the angle is 180
X+5X =180
Thay means,
X=30
Other angle is 150
Supplement angles means. Sum of both the angle is 180
X+5X =180
Thay means,
X=30
Other angle is 150
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The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respe...
Given:
- The area of triangle ABC is 144 cm^2.
- The area of triangle DEF is 81 cm^2.
- The longest side of triangle ABC is 36 cm.
To find:
- The length of the longest side of triangle DEF.
Explanation:
Step 1: Finding the Scale Factor
- The area of a triangle is given by the formula: Area = (1/2) * base * height.
- Since the triangles ABC and DEF are similar, their areas are proportional to the square of their corresponding sides.
- Therefore, we can write: (AB/DE)^2 = Area of ABC/Area of DEF.
- Substituting the given values, we get: (AB/DE)^2 = 144/81.
- Simplifying the equation, we have: (AB/DE)^2 = 16/9.
- Taking the square root of both sides, we get: AB/DE = √(16/9).
- Simplifying further, we have: AB/DE = 4/3.
- This ratio represents the scale factor between the two triangles.
Step 2: Finding the Length of the Longest Side of Triangle DEF
- The longest side of triangle ABC is given as 36 cm.
- Using the scale factor, we can write: AB/DE = 4/3.
- Substituting the values, we have: 36/DE = 4/3.
- Cross-multiplying, we get: 4DE = 36 * 3.
- Simplifying the equation, we have: 4DE = 108.
- Dividing both sides by 4, we get: DE = 27.
- Therefore, the length of the longest side of triangle DEF is 27 cm.
Conclusion:
- The length of the longest side of triangle DEF is 27 cm.
- Hence, the correct answer is option A.
- The area of triangle ABC is 144 cm^2.
- The area of triangle DEF is 81 cm^2.
- The longest side of triangle ABC is 36 cm.
To find:
- The length of the longest side of triangle DEF.
Explanation:
Step 1: Finding the Scale Factor
- The area of a triangle is given by the formula: Area = (1/2) * base * height.
- Since the triangles ABC and DEF are similar, their areas are proportional to the square of their corresponding sides.
- Therefore, we can write: (AB/DE)^2 = Area of ABC/Area of DEF.
- Substituting the given values, we get: (AB/DE)^2 = 144/81.
- Simplifying the equation, we have: (AB/DE)^2 = 16/9.
- Taking the square root of both sides, we get: AB/DE = √(16/9).
- Simplifying further, we have: AB/DE = 4/3.
- This ratio represents the scale factor between the two triangles.
Step 2: Finding the Length of the Longest Side of Triangle DEF
- The longest side of triangle ABC is given as 36 cm.
- Using the scale factor, we can write: AB/DE = 4/3.
- Substituting the values, we have: 36/DE = 4/3.
- Cross-multiplying, we get: 4DE = 36 * 3.
- Simplifying the equation, we have: 4DE = 108.
- Dividing both sides by 4, we get: DE = 27.
- Therefore, the length of the longest side of triangle DEF is 27 cm.
Conclusion:
- The length of the longest side of triangle DEF is 27 cm.
- Hence, the correct answer is option A.
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The area of similar triangles, ABC and DEF are 144cm2 and 81 cm2 respectively. If the longest side of the larger ABC be 36 cm, then the longest side of the smaller DEF is:a)27 cmb)26 cmc)29 cmd)30 cmCorrect answer is option 'A'. Can you explain this answer?
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