Construct a right angle triangle whose hypotenuse is 6 cm long and one of the legs is 4 cm long.

To construct a right triangle with a hypotenuse of 6 cm and one leg of 4 cm, you can use the Pythagorean theorem to find the length of the other leg. The Pythagorean theorem states that in a right 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 lengths of the other two sides.

Let's call the length of the other leg "a."

So, we have:

Hypotenuse^2 = Leg1^2 + Leg2^2

6^2 = 4^2 + a^2

36 = 16 + a^2

Now, subtract 16 from both sides of the equation:

a^2 = 36 - 16
a^2 = 20

To find the length of the other leg, take the square root of both sides:

a = √20

a = 2√5 cm

So, the length of the other leg is 2√5 cm.

Now, you can construct the right triangle with these measurements:

Draw a horizontal line segment of 4 cm (this represents one of the legs).
From one end of the 4 cm line, draw a vertical line segment of 2√5 cm (this represents the other leg).
Connect the open ends of the horizontal and vertical lines to form the hypotenuse, making sure it measures 6 cm.
You now have a right triangle with a hypotenuse of 6 cm and one leg of 4 cm.