One of the acute corners of a right-angled triangle is half the second, and the sum of the hypotenuse and the smaller leg is 10.8 cm.

One of the acute corners of a right-angled triangle is half the second, and the sum of the hypotenuse and the smaller leg is 10.8 cm. Find the hypotenuse.

In a right-angled triangle, the sum of the acute angles is 90 °. If one is twice as large as the other, then one = 60 °, the second 30 °.
the smaller leg lies opposite an angle of 30 °.
Let this smaller leg – x
since a leg, lying opposite an angle of 30 °, is equal to half of the hypotenuse, then the hypotenuse is 2x
2x + x = 10.8 cm
3x = 10.8 cm
x = 3.6 cm
Answer: 3.6 cm