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A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?
- a)16.665
- b)16.565
- c)15.465
- d)14.365
Correct answer is option 'D'. Can you explain this answer?
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A right angled triangle is given. Draw a line that is parallel to the ...
Let ABC be the required triangle cut along DE there is 35% decrease in hypotenuse since both triangles are similar height and base are also get reduced by 35% or new base and height are 65% of original values.
New Area = Area*(65/100)2 = 14.365
Most Upvoted Answer
A right angled triangle is given. Draw a line that is parallel to the ...
Let ABC be the required triangle cut along DE there is 35% decrease in hypotenuse since both triangles are similar height and base are also get reduced by 35% or new base and height are 65% of original values.
New Area = Area*(65/100)2 = 14.365
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A right angled triangle is given. Draw a line that is parallel to the ...
Given:
- A right-angled triangle with a hypotenuse.
- A line parallel to the hypotenuse, creating a smaller triangle.
- The length of the hypotenuse is reduced by 35%.
- The area of the original triangle is 34 cm².
To find:
- The area of the smaller triangle.
Solution:
Step 1: Identify the right-angled triangle and the line parallel to the hypotenuse
- Let's assume the right-angled triangle ABC, where AB is the hypotenuse.
- Draw a line DE parallel to AB, leaving a smaller triangle ADE.
Step 2: Calculate the length of the hypotenuse
- Let the length of AB be 'x'.
- As per the given information, the length of AB is reduced by 35%.
- Therefore, the length of DE will be (x - 0.35x) = 0.65x.
Step 3: Calculate the area of the original triangle
- The area of a right-angled triangle = (1/2) * base * height.
- In triangle ABC, the base is AC and the height is BC.
- Let the base AC be 'a' and the height BC be 'b'.
- Using the Pythagorean theorem, we know that (AB)² = (AC)² + (BC)².
- Since AB is the hypotenuse, AB² = a² + b².
- Given that the area of the original triangle is 34 cm², we have (1/2) * a * b = 34.
Step 4: Calculate the length of DE
- In triangle ADE, AD is the base and DE is the height.
- AD = AC - CD = a - b.
- DE = 0.65x = 0.65(AB).
Step 5: Calculate the area of the smaller triangle
- The area of the smaller triangle ADE = (1/2) * base * height = (1/2) * AD * DE.
- Substituting the values, we get (1/2) * (a - b) * 0.65(AB).
Step 6: Simplify and calculate the area of the smaller triangle
- Using the relation a * b = 68, we can express 'b' in terms of 'a': b = 68/a.
- Substituting this value in the area formula of the smaller triangle, we get (1/2) * (a - 68/a) * 0.65(AB).
- Further simplifying, we get (0.65/2) * (a² - 68) * (AB/a).
- As AB/a is the hypotenuse reduction factor, we can rewrite the formula as (0.65/2) * (a² - 68) * 0.65x.
- Simplifying further, we get (0.65/2) * 0.65 * (a² - 68) * x.
- The factor (0.65/2) * 0.65 is approximately 0.21125.
Step 7: Calculate the area of the
- A right-angled triangle with a hypotenuse.
- A line parallel to the hypotenuse, creating a smaller triangle.
- The length of the hypotenuse is reduced by 35%.
- The area of the original triangle is 34 cm².
To find:
- The area of the smaller triangle.
Solution:
Step 1: Identify the right-angled triangle and the line parallel to the hypotenuse
- Let's assume the right-angled triangle ABC, where AB is the hypotenuse.
- Draw a line DE parallel to AB, leaving a smaller triangle ADE.
Step 2: Calculate the length of the hypotenuse
- Let the length of AB be 'x'.
- As per the given information, the length of AB is reduced by 35%.
- Therefore, the length of DE will be (x - 0.35x) = 0.65x.
Step 3: Calculate the area of the original triangle
- The area of a right-angled triangle = (1/2) * base * height.
- In triangle ABC, the base is AC and the height is BC.
- Let the base AC be 'a' and the height BC be 'b'.
- Using the Pythagorean theorem, we know that (AB)² = (AC)² + (BC)².
- Since AB is the hypotenuse, AB² = a² + b².
- Given that the area of the original triangle is 34 cm², we have (1/2) * a * b = 34.
Step 4: Calculate the length of DE
- In triangle ADE, AD is the base and DE is the height.
- AD = AC - CD = a - b.
- DE = 0.65x = 0.65(AB).
Step 5: Calculate the area of the smaller triangle
- The area of the smaller triangle ADE = (1/2) * base * height = (1/2) * AD * DE.
- Substituting the values, we get (1/2) * (a - b) * 0.65(AB).
Step 6: Simplify and calculate the area of the smaller triangle
- Using the relation a * b = 68, we can express 'b' in terms of 'a': b = 68/a.
- Substituting this value in the area formula of the smaller triangle, we get (1/2) * (a - 68/a) * 0.65(AB).
- Further simplifying, we get (0.65/2) * (a² - 68) * (AB/a).
- As AB/a is the hypotenuse reduction factor, we can rewrite the formula as (0.65/2) * (a² - 68) * 0.65x.
- Simplifying further, we get (0.65/2) * 0.65 * (a² - 68) * x.
- The factor (0.65/2) * 0.65 is approximately 0.21125.
Step 7: Calculate the area of the
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A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer?
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A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer?.
A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer?.
Solutions for A right angled triangle is given. Draw a line that is parallel to the hypotenuse, leaving a smaller triangle. There was a 35% reduction in the length of the hypotenuse of the triangle. If the area of the original triangle was 34 cm2, what is the area (in cm2) of the smaller triangle?a)16.665 b)16.565 c)15.465 d)14.365Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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