In a rectangular triangle, the median drawn to the hypotenuse is 6, determine the perimeter

In a rectangular triangle, the median drawn to the hypotenuse is 6, determine the perimeter of the triangle if the ratio of the catites is 3/4.

Since the median CD was drawn at the hypotenuse, the length of the median is half the length of the hypotenuse AB.

CD = AB / 2, then AB = CD * 2 = 6 * 2 = 12 cm.

Let the length of the smaller leg be 3 * X cm, then the length of the larger leg will be 4 * X cm.

For triangle ABC, we apply the Pythagorean theorem.

AB ^ 2 = AC ^ 2 + BC ^ 2.

144 = 16 * X ^ 2 + 9 * X ^ 2 = 25 * X ^ 2.

X2 = 144/25.

X = 12/5 = 2.4.

Then AC = 4 * 2.4 = 9.6 cm.

BC = 3 * 2.4 = 7.2 cm.

Determine the perimeter of the triangle.

Ravs = 12 + 9.6 + 7.2 = 28.8 cm.

Answer: The perimeter of the triangle is 28.8 cm.