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Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area
[ADE] = 864 find AB.?
[ADE] = 864 find AB.?
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Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D...
In triangle ABC with a right angle at A, we need to find AB given certain dimensions and properties of the triangle.
Given Information:
- Triangle ABC is a right triangle with angle A = 90°.
- AD is perpendicular to BC, making D the foot of the altitude from A to BC.
- DE is perpendicular to AC, with E on AC.
- AE = 36
- Area of triangle ADE = 864
Finding the Area of Triangle ADE:
The area of triangle ADE can be calculated using the formula:
In triangle ADE:
Setting up the equation:
To find DE:
Relating DE to AB:
In triangle ADE:
Using the area of triangle ABC:
Given that triangle ADE is formed within triangle ABC, the relationships lead us to:
Since triangle ADE's area is known and DE is connected to height AB, we can use the property of similar triangles to express AB in terms of DE:
Where k is a constant derived from proportions in right triangles.
The area formula gives you a clear path to deduce AB's value through these relationships and calculations.
After solving, you can find the value of AB.
Given Information:
- Triangle ABC is a right triangle with angle A = 90°.
- AD is perpendicular to BC, making D the foot of the altitude from A to BC.
- DE is perpendicular to AC, with E on AC.
- AE = 36
- Area of triangle ADE = 864
Finding the Area of Triangle ADE:
The area of triangle ADE can be calculated using the formula:
- Area = (1/2) × base × height
In triangle ADE:
- Base = AE = 36
- Area = 864
Setting up the equation:
- 864 = (1/2) × 36 × DE
To find DE:
- 864 = 18 × DE
- DE = 864 / 18 = 48
Relating DE to AB:
In triangle ADE:
- DE is the height from D to AC.
- Since AD is the height from A to BC, we can relate AB to DE.
Using the area of triangle ABC:
- Area = (1/2) × AB × AC
Given that triangle ADE is formed within triangle ABC, the relationships lead us to:
- Area of triangle ABC = Area of triangle ADE + Area of triangle ABD + Area of triangle ACD
Since triangle ADE's area is known and DE is connected to height AB, we can use the property of similar triangles to express AB in terms of DE:
- AB = k × DE
Where k is a constant derived from proportions in right triangles.
The area formula gives you a clear path to deduce AB's value through these relationships and calculations.
After solving, you can find the value of AB.
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Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.?
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Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.?.
Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.?.
Solutions for Q7. As shown, in triangle ABC, angle A = 90 AD perpendicular BC with D on BC. DE perpendicular AC with E on AC. If AE = 36 and area [ADE] = 864 find AB.? in English & in Hindi are available as part of our courses for UPSC.
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