step 1- draw line segment AB of 12cm. draw a ray AX making 90* with AB.step 2-cut a line segment AD of 18 cm (as the sum of the other 2 sides is 18 cm from ray AX.step 3- join DB & make an angle DBY equal to ADB.step 4- let BY intersect AX at C . join AC,BCABC is a required triangle.

Constructing a Right Triangle with Given Measurements

To construct a right triangle with a base of 12cm and the sum of its hypotenuse and the other side being 18cm, follow these steps:

Step 1: Draw the Base
Start by drawing a line segment of 12cm to represent the base of the triangle.

Step 2: Determine the Length of the Hypotenuse and Other Side
Since the sum of the hypotenuse and the other side is 18cm, let's assume the length of the hypotenuse is x cm. This means the length of the other side would be 18cm - x cm.

Step 3: Construct the Right Triangle
Using a compass and ruler, construct a perpendicular line from one endpoint of the base. The length of this line should be the length of the other side (18cm - x cm).

Next, construct a line segment from the opposite endpoint of the base to the endpoint of the perpendicular line. This line segment will represent the hypotenuse of the right triangle and should be x cm long.

Step 4: Verify the Triangle
Check that the angles formed are a right angle where the base and the perpendicular line intersect.

By following these steps, you can construct a right triangle with a base of 12cm and the sum of its hypotenuse and the other side being 18cm.