Sides of triangles are given below. Determine which of them are right triangles. In case of a right triangle,write the length of its hypotenuse.
$7 \, cm, 24 \, cm, 25 \, cm$
$7 \, cm, 24 \, cm, 25 \, cm$
(A) The given sides of the triangle are $7 \, cm, 24 \, cm,$ and $25 \, cm$.
To check if it is a right-angled triangle,we use the converse of the Pythagoras theorem,which states that if the square of the longest side is equal to the sum of the squares of the other two sides,then the triangle is a right-angled triangle.
First,we calculate the squares of the given sides:
$7^2 = 49$
$24^2 = 576$
$25^2 = 625$
Now,we check if the sum of the squares of the two smaller sides equals the square of the largest side:
$49 + 576 = 625$
Since $7^2 + 24^2 = 25^2$,the given sides satisfy the Pythagoras theorem.
Therefore,the triangle is a right-angled triangle.
The longest side of a right-angled triangle is its hypotenuse. Thus,the length of the hypotenuse is $25 \, cm$.
To check if it is a right-angled triangle,we use the converse of the Pythagoras theorem,which states that if the square of the longest side is equal to the sum of the squares of the other two sides,then the triangle is a right-angled triangle.
First,we calculate the squares of the given sides:
$7^2 = 49$
$24^2 = 576$
$25^2 = 625$
Now,we check if the sum of the squares of the two smaller sides equals the square of the largest side:
$49 + 576 = 625$
Since $7^2 + 24^2 = 25^2$,the given sides satisfy the Pythagoras theorem.
Therefore,the triangle is a right-angled triangle.
The longest side of a right-angled triangle is its hypotenuse. Thus,the length of the hypotenuse is $25 \, cm$.
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