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A paper sheet is in the shape of a right angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2 then area of smaller triangle will be ______ cm2.
Correct answer is between '15,16'. Can you explain this answer?
Verified Answer
A paper sheet is in the shape of aright angle triangle and cut along a...
Let PQR is the initial triangle and SQT is the final triangle.
ΔPQR is similar to ΔSQT
∵ ST = 0.75 PR
∴ SQ = 0.75 PQ
And QT = 0.75 QR
Most Upvoted Answer
A paper sheet is in the shape of aright angle triangle and cut along a...
Analysis:
To solve this problem, we need to understand the relationship between the areas of similar triangles and the relationship between the lengths of corresponding sides.
Given:
- The initial triangle is a right-angled triangle.
- The initial area of the triangle is 28 cm^2.
- There is a 25% reduction in the length of the hypotenuse.
Approach:
1. Let's assume the initial triangle has sides a, b, and c, with c being the hypotenuse.
2. The area of a right-angled triangle can be calculated using the formula: Area = (1/2) * base * height.
3. In this case, the base and height of the triangle are a and b, respectively.
4. So, the initial area of the triangle is given as: 28 = (1/2) * a * b.
5. Now, let's consider the smaller triangle formed after cutting along a line parallel to the hypotenuse.
6. The length of the hypotenuse of the smaller triangle will be 25% less than the length of the hypotenuse of the initial triangle.
7. Therefore, the length of the hypotenuse of the smaller triangle will be (0.75 * c).
8. The ratio of the lengths of corresponding sides of similar triangles is equal.
9. So, we can write the following proportion: (0.75 * c) / c = a' / a, where a' is the length of the base of the smaller triangle.
10. Solving the proportion, we get: a' = 0.75 * a.
11. Similarly, we can write another proportion: (0.75 * c) / c = b' / b, where b' is the length of the height of the smaller triangle.
12. Solving this proportion, we get: b' = 0.75 * b.
13. The area of the smaller triangle can be calculated using the formula: Area' = (1/2) * a' * b'.
14. Substituting the values of a' and b' from steps 10 and 12, we get: Area' = (1/2) * (0.75 * a) * (0.75 * b).
15. Simplifying the expression, we get: Area' = 0.5625 * a * b.
16. Now, we can substitute the initial area of the triangle (28) into the equation: 0.5625 * a * b = 28.
17. Solving this equation, we get: a * b = 49.778.
18. Therefore, the area of the smaller triangle is approximately 49.778 * 0.5625 = 27.984375 cm^2.
19. Rounding off the area to the nearest whole number, we get 28 cm^2 as the area of the smaller triangle.
Conclusion:
The area of the smaller triangle formed after cutting the initial right-angled triangle along a line parallel to the hypotenuse is approximately 28 cm^2.
To solve this problem, we need to understand the relationship between the areas of similar triangles and the relationship between the lengths of corresponding sides.
Given:
- The initial triangle is a right-angled triangle.
- The initial area of the triangle is 28 cm^2.
- There is a 25% reduction in the length of the hypotenuse.
Approach:
1. Let's assume the initial triangle has sides a, b, and c, with c being the hypotenuse.
2. The area of a right-angled triangle can be calculated using the formula: Area = (1/2) * base * height.
3. In this case, the base and height of the triangle are a and b, respectively.
4. So, the initial area of the triangle is given as: 28 = (1/2) * a * b.
5. Now, let's consider the smaller triangle formed after cutting along a line parallel to the hypotenuse.
6. The length of the hypotenuse of the smaller triangle will be 25% less than the length of the hypotenuse of the initial triangle.
7. Therefore, the length of the hypotenuse of the smaller triangle will be (0.75 * c).
8. The ratio of the lengths of corresponding sides of similar triangles is equal.
9. So, we can write the following proportion: (0.75 * c) / c = a' / a, where a' is the length of the base of the smaller triangle.
10. Solving the proportion, we get: a' = 0.75 * a.
11. Similarly, we can write another proportion: (0.75 * c) / c = b' / b, where b' is the length of the height of the smaller triangle.
12. Solving this proportion, we get: b' = 0.75 * b.
13. The area of the smaller triangle can be calculated using the formula: Area' = (1/2) * a' * b'.
14. Substituting the values of a' and b' from steps 10 and 12, we get: Area' = (1/2) * (0.75 * a) * (0.75 * b).
15. Simplifying the expression, we get: Area' = 0.5625 * a * b.
16. Now, we can substitute the initial area of the triangle (28) into the equation: 0.5625 * a * b = 28.
17. Solving this equation, we get: a * b = 49.778.
18. Therefore, the area of the smaller triangle is approximately 49.778 * 0.5625 = 27.984375 cm^2.
19. Rounding off the area to the nearest whole number, we get 28 cm^2 as the area of the smaller triangle.
Conclusion:
The area of the smaller triangle formed after cutting the initial right-angled triangle along a line parallel to the hypotenuse is approximately 28 cm^2.
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A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer?.
A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A paper sheet is in the shape of aright angle triangle and cut along a line parallel to hypotenuse leaving a smaller triangle. There was 25% reduction in the length of the hypotenuse of the triangle. If area of triangle initially was 28 cm2then area of smaller triangle will be ______ cm2.Correct answer is between '15,16'. Can you explain this answer?.
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