In a right-angled triangle if the hypotenuse is 20 cm and the ratio of the other two sides is 4:3, the length of the sides are:
16 cm and 12 cm
Let the two sides of the right-angled triangle be \(4x\) and \(3x\), where \(x\) is a constant. According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. In this case, the hypotenuse is 20 cm.
Therefore, we can write the equation:
\((4x)^2 + (3x)^2 = 20^2\)
Simplifying the equation:
\(16x^2 + 9x^2 = 400\)
\(25x^2 = 400\)
Dividing both sides by 25:
\(x^2 = \frac{400}{25} = 16\)
Taking the square root of both sides:
\(x = 4\)
Now, we can find the lengths of the two sides:
Side 1: \(4x = 4 \times 4 = 16\) cm
Side 2: \(3x = 3 \times 4 = 12\) cm
Therefore, the lengths of the sides are 16 cm and 12 cm.
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