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Pythagoras theorem
Posted by Vaishnavi on June 23, 2023 at 2:18 pmA right angled triangle having base as 6 cm and the side opposite to right angle is 10 cm. Find the height of the right angled triangle.
Priti replied 3 months, 1 week ago 5 Members · 4 Replies 
4 Replies

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To find the height of a rightangled triangle, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the base of the triangle is 6 cm, and the side opposite the right angle is 10 cm. Let’s denote the height as ‘h’.
According to the Pythagorean theorem:
(base)^2 + (height)^2 = (hypotenuse)^2
Substituting the known values:
6^2 + h^2 = 10^2
36 + h^2 = 100
h^2 = 100 – 36
h^2 = 64
Taking the square root of both sides:
h = √64
h = 8 cm
Therefore, the height of the rightangled triangle is 8 cm.

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According to the given question,
base = 6cm
hypotenuse= 10cm (as opposite to right angle)
Height=
h=root(C2−b2)
h=root(10square−6square)h=root(10036)
h=root(64)
h=8cm
 This reply was modified 3 months, 1 week ago by Shruti Thakar.
 This reply was modified 3 months, 1 week ago by Shruti Thakar.

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The Pythagorean theorem states that – “In a right angled triangle, the sum of squares of base and perpendicular is equal to the square of hypotenuse.”
In this question, the hypoetenuse is given 10cm and the base is goven 6cm.
According to pythagorean theorem,
Hypotenuse^2= Base^2 + Perpendicular^2
Therefore,
10^2 = 6^2 + Perpendicular^2
This implies,
100 = 36 + Perpendicular^2
As a result,
Perpendicular^2 = 64
Taking square root on both sides,
Perpendicular = 8cm
Answer: The perpendicular is of 8cm.
 This reply was modified 3 months, 1 week ago by Ashutosh Kumar Choudhary.

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We know that in a rightangled triangle: (Hypotenuse)² = (Perpendicular Height)² +(Base)²
Given: Base=6cm, and side opposite to right angle triangle is termed as Hypotenuse, therefore, Hypotenuse =10 cm.
(Hypotenuse)² = (Perpendicular Height)² +(Base)²
=> (P)² = (H)² (B)²
=> (P)² = (10)² – (6)²
=> (P)² = 100 36
=> (P)² = 64
=> (P) = √64
=> (P)² = 8 cm
Hence, the Height of the right angle triangle = 8 cm
 This reply was modified 3 months, 1 week ago by Priti Ranjan.