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The perimeter formula of a right isosceles triangle with base length 'b' and height 'h' is:
- a)Perimeter of Right Isosceles Triangle = b + h
- b)Perimeter of Right Isosceles Triangle = 2b + h
- c)Perimeter of Right Isosceles Triangle = b + 2h
- d)Perimeter of Right Isosceles Triangle = h + 2l
Correct answer is option 'C'. Can you explain this answer?
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The perimeter formula of a right isosceles triangle with base length b...
The perimeter formula of a right isosceles triangle with base length 'b' and height 'h' is given as Perimeter of Right Isosceles Triangle = b + 2h. This means you add the base length 'b' with twice the height 'h' to calculate the perimeter.
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The perimeter formula of a right isosceles triangle with base length b...
The correct answer is option 'C': Perimeter of Right Isosceles Triangle = b * 2h.
Explanation:
A right isosceles triangle is a triangle with one right angle (90 degrees) and two equal side lengths. In this case, the base length is represented by 'b' and the height is represented by 'h'.
To find the perimeter of any triangle, we need to add up the lengths of all three sides.
In a right isosceles triangle, the two equal side lengths are the base and the height, and the hypotenuse is the longest side.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we can find the length of the hypotenuse (let's call it 'l'):
l^2 = b^2 + h^2
Taking the square root of both sides, we get:
l = sqrt(b^2 + h^2)
Now, the perimeter is the sum of all three sides:
Perimeter = b + h + l
Substituting the value of 'l' from the previous equation, we get:
Perimeter = b + h + sqrt(b^2 + h^2)
However, in a right isosceles triangle, the base and height are equal. So, we can simplify the equation further:
Perimeter = b + b + sqrt(b^2 + b^2)
= 2b + sqrt(2b^2)
= 2b + b(sqrt(2))
Therefore, the correct formula for the perimeter of a right isosceles triangle is:
Perimeter of Right Isosceles Triangle = b * (2 + sqrt(2)).
So, option 'C': Perimeter of Right Isosceles Triangle = b * 2h is incorrect.
The correct answer is option 'D': Perimeter of Right Isosceles Triangle = b * (2 + sqrt(2)).
Explanation:
A right isosceles triangle is a triangle with one right angle (90 degrees) and two equal side lengths. In this case, the base length is represented by 'b' and the height is represented by 'h'.
To find the perimeter of any triangle, we need to add up the lengths of all three sides.
In a right isosceles triangle, the two equal side lengths are the base and the height, and the hypotenuse is the longest side.
To find the length of the hypotenuse, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Using this theorem, we can find the length of the hypotenuse (let's call it 'l'):
l^2 = b^2 + h^2
Taking the square root of both sides, we get:
l = sqrt(b^2 + h^2)
Now, the perimeter is the sum of all three sides:
Perimeter = b + h + l
Substituting the value of 'l' from the previous equation, we get:
Perimeter = b + h + sqrt(b^2 + h^2)
However, in a right isosceles triangle, the base and height are equal. So, we can simplify the equation further:
Perimeter = b + b + sqrt(b^2 + b^2)
= 2b + sqrt(2b^2)
= 2b + b(sqrt(2))
Therefore, the correct formula for the perimeter of a right isosceles triangle is:
Perimeter of Right Isosceles Triangle = b * (2 + sqrt(2)).
So, option 'C': Perimeter of Right Isosceles Triangle = b * 2h is incorrect.
The correct answer is option 'D': Perimeter of Right Isosceles Triangle = b * (2 + sqrt(2)).
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The perimeter formula of a right isosceles triangle with base length b and height h is:a)Perimeter of Right Isosceles Triangle = b + hb)Perimeter of Right Isosceles Triangle = 2b + hc)Perimeter of Right Isosceles Triangle = b + 2hd)Perimeter of Right Isosceles Triangle = h + 2lCorrect answer is option 'C'. Can you explain this answer?
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