A right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.

Q: A right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.

Pythagorean Theorem Formula\nThe Pythagorean theorem states that in a right-angled 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. \na^2 + b^2 = c^2 \nwhere a and b are the lengths of the other two sides, and c is the length of the hypotenuse. Given Values\nBase (a) = 5 cm\nHeight (b) = 12 cm Calculation\nTo find the length of the hypotenuse, we can use the Pythagorean theorem: \nc^2 = a^2 + b^2\nc^2 = 5^2 + 12^2\nc^2 = 25 + 144\nc^2 = 169 Finding the Length of the Hypotenuse\nTo find the length of the hypotenuse, we take the square root of both sides: \nc = √169\nc = 13 Conclusion\nTherefore, the length of the hypotenuse is 13 cm.

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Pythagorean Theorem Formula
The Pythagorean theorem states that in a right-angled 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. 
a^2 + b^2 = c^2 
where a and b are the lengths of the other two sides, and c is the length of the hypotenuse. Given Values
Base (a) = 5 cm
Height (b) = 12 cm Calculation
To find the length of the hypotenuse, we can use the Pythagorean theorem: 
c^2 = a^2 + b^2
c^2 = 5^2 + 12^2
c^2 = 25 + 144
c^2 = 169 Finding the Length of the Hypotenuse
To find the length of the hypotenuse, we take the square root of both sides: 
c = √169
c = 13 Conclusion
Therefore, the length of the hypotenuse is 13 cm.

CBSE · Class 10 · Mathematics · Introduction to TrigonometryA right-angled triangle has a base of 5 cm and a height of 12 cm. Calculate the length of the hypotenuse using the Pythagorean theorem.

Pythagorean Theorem

Formula\nThe Pythagorean theorem states that in a right-angled 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.

Given Values\nBase (a) = 5 cm\nHeight (b) = 12 cm

Calculation\nTo find the length of the hypotenuse, we can use the Pythagorean theorem:

Finding the Length of the Hypotenuse\nTo find the length of the hypotenuse, we take the square root of both sides:

Conclusion\nTherefore, the length of the hypotenuse is 13 cm.