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An isosceles right angled triangle with length of its equal sides being 30 cm, is rotated 180° about its centroid to form a new triangle. Find the area of the region common to the original and the new triangles.
(2015)
- a)275 sq. cm
- b)300 sq. cm
- c)375 sq. cm
- d)350 sq. cm
Correct answer is option 'B'. Can you explain this answer?
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When an isosceles right-angled triangle is rotated by 180 degrees, it will result in the same triangle being reflected or flipped over. This means that the position of the vertices will change, but the shape and size of the triangle will remain the same.
In this case, the triangle has two equal sides with a length of 30 cm each. The third side, the hypotenuse, can be found using the Pythagorean theorem.
Let's assume the two equal sides are the legs of the triangle, and the hypotenuse is the side opposite the right angle.
Using the Pythagorean theorem:
Leg^2 + Leg^2 = Hypotenuse^2
30^2 + 30^2 = Hypotenuse^2
900 + 900 = Hypotenuse^2
1800 = Hypotenuse^2
Hypotenuse = √1800
Hypotenuse ≈ 42.43 cm
So, the length of the hypotenuse of the isosceles right-angled triangle is approximately 42.43 cm.
When this triangle is rotated 180 degrees, the shape and size of the triangle will remain the same. However, the position of the vertices will change. The two equal sides will still have a length of 30 cm each, and the hypotenuse will still have a length of approximately 42.43 cm.
In this case, the triangle has two equal sides with a length of 30 cm each. The third side, the hypotenuse, can be found using the Pythagorean theorem.
Let's assume the two equal sides are the legs of the triangle, and the hypotenuse is the side opposite the right angle.
Using the Pythagorean theorem:
Leg^2 + Leg^2 = Hypotenuse^2
30^2 + 30^2 = Hypotenuse^2
900 + 900 = Hypotenuse^2
1800 = Hypotenuse^2
Hypotenuse = √1800
Hypotenuse ≈ 42.43 cm
So, the length of the hypotenuse of the isosceles right-angled triangle is approximately 42.43 cm.
When this triangle is rotated 180 degrees, the shape and size of the triangle will remain the same. However, the position of the vertices will change. The two equal sides will still have a length of 30 cm each, and the hypotenuse will still have a length of approximately 42.43 cm.
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An isosceles right angled triangle with length of its equal sides being 30 cm, is rotated 180° about its centroid to form a new triangle. Find the area of the region common to the original and the new triangles.(2015)a)275 sq. cmb)300 sq. cmc)375 sq. cmd)350 sq. cmCorrect answer is option 'B'. Can you explain this answer?
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