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Smallest side of a right angled triangle is 6 cm less than the side of a square of perimeter 60 cm. Second largest side of the right angled triangle is 4 cm less than the length of rectangle of area 80 sq. cm and breadth 5 cm. What is the largest side of the right angled triangle?
- a)10cm
- b)9cm
- c)12cm
- d)15cm
- e)None of these
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
Smallest side of a right angled triangle is 6 cm less than the side of...
Side of 1st square = 60/4 = 15 cm.
Smallest side of right angled triangle= 15 −6 = 9 cm.
Length of 2nd rectangle = 80/5 = 16 cm.
Second largest side of the 1strectangle = 16−4 = 12 cm.
Largest side = hypotenuse=√92+122=15cm
Smallest side of right angled triangle= 15 −6 = 9 cm.
Length of 2nd rectangle = 80/5 = 16 cm.
Second largest side of the 1strectangle = 16−4 = 12 cm.
Largest side = hypotenuse=√92+122=15cm
Most Upvoted Answer
Smallest side of a right angled triangle is 6 cm less than the side of...
Given perimeter of square is 60cm then each side of square will be 15cm. then smallest side of right angled triangle will be 15-6=9cm.
Also given breadth of rectangle is 5cm and area of rectangle is 80 sq.cm then length of rectangle will be 80/5=16cm. So second largest side of right angled triangle will be 16-4=12cm.
Then hypotenuse of right angled triangle will be 15cm.
Also given breadth of rectangle is 5cm and area of rectangle is 80 sq.cm then length of rectangle will be 80/5=16cm. So second largest side of right angled triangle will be 16-4=12cm.
Then hypotenuse of right angled triangle will be 15cm.
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Smallest side of a right angled triangle is 6 cm less than the side of...
Given information:
- The smallest side of a right-angled triangle is 6 cm less than the side of a square with a perimeter of 60 cm.
- The second largest side of the right-angled triangle is 4 cm less than the length of a rectangle with an area of 80 sq. cm and breadth 5 cm.
To find:
The largest side of the right-angled triangle.
Let's solve this step by step:
1. Determine the side of the square:
The perimeter of a square is given by the formula: Perimeter = 4 * side.
Given that the perimeter of the square is 60 cm, we can write the equation as:
4 * side = 60
Dividing both sides by 4, we get:
side = 60 / 4 = 15 cm
2. Determine the smallest side of the right-angled triangle:
The smallest side of the right-angled triangle is 6 cm less than the side of the square.
So, the smallest side of the right-angled triangle = side of the square - 6 cm = 15 cm - 6 cm = 9 cm.
3. Determine the area of the rectangle:
The area of a rectangle is given by the formula: Area = Length * Breadth.
Given that the area of the rectangle is 80 sq. cm and the breadth is 5 cm, we can write the equation as:
80 = Length * 5
Dividing both sides by 5, we get:
Length = 80 / 5 = 16 cm
4. Determine the second largest side of the right-angled triangle:
The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle.
So, the second largest side of the right-angled triangle = Length of the rectangle - 4 cm = 16 cm - 4 cm = 12 cm.
5. Determine the largest side of the right-angled triangle:
In a right-angled triangle, the largest side is the hypotenuse.
Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the hypotenuse.
Let the smallest side be 'a' and the second largest side be 'b'.
According to the Pythagorean theorem, a^2 + b^2 = hypotenuse^2.
Substituting the values, we get:
9^2 + 12^2 = hypotenuse^2
81 + 144 = hypotenuse^2
225 = hypotenuse^2
Taking the square root of both sides, we get:
hypotenuse = √225 = 15 cm
Therefore, the largest side of the right-angled triangle is 15 cm. Hence, the correct answer is option D.
- The smallest side of a right-angled triangle is 6 cm less than the side of a square with a perimeter of 60 cm.
- The second largest side of the right-angled triangle is 4 cm less than the length of a rectangle with an area of 80 sq. cm and breadth 5 cm.
To find:
The largest side of the right-angled triangle.
Let's solve this step by step:
1. Determine the side of the square:
The perimeter of a square is given by the formula: Perimeter = 4 * side.
Given that the perimeter of the square is 60 cm, we can write the equation as:
4 * side = 60
Dividing both sides by 4, we get:
side = 60 / 4 = 15 cm
2. Determine the smallest side of the right-angled triangle:
The smallest side of the right-angled triangle is 6 cm less than the side of the square.
So, the smallest side of the right-angled triangle = side of the square - 6 cm = 15 cm - 6 cm = 9 cm.
3. Determine the area of the rectangle:
The area of a rectangle is given by the formula: Area = Length * Breadth.
Given that the area of the rectangle is 80 sq. cm and the breadth is 5 cm, we can write the equation as:
80 = Length * 5
Dividing both sides by 5, we get:
Length = 80 / 5 = 16 cm
4. Determine the second largest side of the right-angled triangle:
The second largest side of the right-angled triangle is 4 cm less than the length of the rectangle.
So, the second largest side of the right-angled triangle = Length of the rectangle - 4 cm = 16 cm - 4 cm = 12 cm.
5. Determine the largest side of the right-angled triangle:
In a right-angled triangle, the largest side is the hypotenuse.
Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can find the hypotenuse.
Let the smallest side be 'a' and the second largest side be 'b'.
According to the Pythagorean theorem, a^2 + b^2 = hypotenuse^2.
Substituting the values, we get:
9^2 + 12^2 = hypotenuse^2
81 + 144 = hypotenuse^2
225 = hypotenuse^2
Taking the square root of both sides, we get:
hypotenuse = √225 = 15 cm
Therefore, the largest side of the right-angled triangle is 15 cm. Hence, the correct answer is option D.
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