Question

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

• A. 5 cm
• B. 12 cm
• C. 13 cm
• D. 20 cm

Answer 1

The correct option is C 13 cm

Steps to construct the required triangle are as follows :

Step 1: Draw the line segment AB of length 12 cm .Draw a ray AX making an angle ${90}^{\circ }$ with the line segment AB.
Step 2: Cut a line segment AD of 18 cm ( as the sum of the other sides is 18) on the ray AX.
Step 3: Join DB.
Step 4: Construct perpendicular bisector MN of BD, intersecting the line AD at C. Join BC
Step 5: Then $\Delta ABC$ is the required triangle.

Now, take a ruler a measure the length of BC (hypotenuse) which will be 13 cm.