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The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?
- a)6 cm2
- b)12 cm2
- c)18 cm2
- d)24 cm2
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
The square of the length of a rod AB is 72 cm2. If we place the rod in...
Square of the length of a rod AB is given as 72 cm2. We need to find the maximum possible area of the triangle formed by the rod, the edge between the walls, and the floor.
Let's solve this step by step.
Step 1: Find the length of the rod AB.
Given, square of the length of AB = 72 cm2
Taking the square root of both sides, we get:
Length of AB = √(72 cm2)
= √(36 × 2 cm2)
= 6√2 cm
Step 2: Draw a diagram.
To visualize the problem, draw a diagram representing a corner of the room. Place the rod AB in such a way that end A is on the edge between the two walls and end B is on the floor.
Step 3: Calculate the height of the triangle.
The height of the triangle is equal to the length of AB, which is 6√2 cm.
Step 4: Calculate the base of the triangle.
The base of the triangle is the edge between the walls, which is equal to the length of AB, i.e., 6√2 cm.
Step 5: Calculate the area of the triangle.
The area of a triangle can be calculated using the formula:
Area = (1/2) × base × height
Substituting the values, we get:
Area = (1/2) × (6√2 cm) × (6√2 cm)
= (1/2) × (6 cm) × (√2 cm) × (6 cm) × (√2 cm)
= (1/2) × (6 cm × 6 cm) × (√2 cm × √2 cm)
= (1/2) × (36 cm2) × (2 cm)
= 18 cm2
Therefore, the maximum possible area of the triangle formed by the rod AB, the edge between the walls, and the floor is 18 cm2.
Hence, the correct answer is option C) 18 cm2.
Let's solve this step by step.
Step 1: Find the length of the rod AB.
Given, square of the length of AB = 72 cm2
Taking the square root of both sides, we get:
Length of AB = √(72 cm2)
= √(36 × 2 cm2)
= 6√2 cm
Step 2: Draw a diagram.
To visualize the problem, draw a diagram representing a corner of the room. Place the rod AB in such a way that end A is on the edge between the two walls and end B is on the floor.
Step 3: Calculate the height of the triangle.
The height of the triangle is equal to the length of AB, which is 6√2 cm.
Step 4: Calculate the base of the triangle.
The base of the triangle is the edge between the walls, which is equal to the length of AB, i.e., 6√2 cm.
Step 5: Calculate the area of the triangle.
The area of a triangle can be calculated using the formula:
Area = (1/2) × base × height
Substituting the values, we get:
Area = (1/2) × (6√2 cm) × (6√2 cm)
= (1/2) × (6 cm) × (√2 cm) × (6 cm) × (√2 cm)
= (1/2) × (6 cm × 6 cm) × (√2 cm × √2 cm)
= (1/2) × (36 cm2) × (2 cm)
= 18 cm2
Therefore, the maximum possible area of the triangle formed by the rod AB, the edge between the walls, and the floor is 18 cm2.
Hence, the correct answer is option C) 18 cm2.
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Community Answer
The square of the length of a rod AB is 72 cm2. If we place the rod in...
From the given question Area of right triangle is maximum, when base is equal to perpendicular.
∴ = 1/2 x 6 x 6 = 18 cm2
So the maximum possible area of the triangle formed by rod is 18 cm2.
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The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer?
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The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer?.
The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The square of the length of a rod AB is 72 cm2. If we place the rod in the corner of a room, so that the end A is always on the edge between the two walls of the corner and the end B is always on the floor, what is the maximum possible area of the triangle formed by the rod, the edge between the walls and the floor?a)6 cm2b)12 cm2c)18 cm2d)24 cm2Correct answer is option 'C'. Can you explain this answer?.
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