Question

Construct a right triangle whose base is 12 cm and the sum of its hypotenuse and other side is 18 cm.

Answer 1

Hint:
We have to construct a right-angle triangle whose base is 12 cm and the sum of its hypotenuse and the other side which is perpendicular is 18cm. so, we will use the geometry to construct it. First, we will draw the line segment AB (base) of the given dimension. Next, we will draw a ray AX which will make the right-angle with base. After this cut the line segment AD of length 18 cm from ray AX. Now, we will join the points B and D and we will get the line BD and we will make the angles DBY equal to ADB such that the line BY intersect the ray AX at some point C. after this we will join AC and BC. Hence, this will be the required triangle.

Complete step by step solution:
We will first consider the given information in order to construct the triangle that is a right-angle triangle whose base is 12 cm and the sum of its hypotenuse and the other side which is perpendicular is 18cm.
We will first draw a line segment AB of length 12cm that is the base of the right triangle.

Now, draw a line from point A and name the line as AX such that the line AX makes right-angle with AB.

Next, we will cut a line segment AD of length 18cm from the line AX.

After this, we will join the points B and D and get the line BD.

Further, we will make angles DBY equal to ADB such that the line BY originated from B intersect AX at C.
Next, we will join AC and BC.
Thus, we get the figure as follows,

Hence, triangle ABC is the required triangle.

Note:
While constructing the right triangle, do remember to make the perpendicular or the 90 degrees angle with the base. As C cuts the line AX implies that AC and BC together form the sum as 18cm by using the congruence property of triangles.