the square of the hypotenuse of an isosceles right angled triangle is 98 sq. cm. what is the length of each side ?
2s^2 = 98
s = 7
To find the length of each side of an isosceles right-angled triangle, we need to use the Pythagorean theorem. The Pythagorean theorem states that in a right-angled 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 problem states that the square of the hypotenuse is 98 sq. cm. Let's call the length of each side of the triangle "x".
According to the Pythagorean theorem, we can set up the equation as follows:
x^2 + x^2 = 98
Simplifying the equation, we have:
2x^2 = 98
Now, we can rearrange the equation to solve for x. Divide both sides of the equation by 2:
x^2 = 49
Taking the square root of both sides, we get:
x = √49
Since we are dealing with a physical length, we take the positive square root:
x = 7
Therefore, the length of each side of the isosceles right-angled triangle is 7 cm.