Question

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

Answer 1

Hint: Start by constructing a base, followed by a perpendicular line to the base at one of the ends. Then mark the point where the distance of the perpendicular from the base is 18cm and join the point to the other end of the base. Draw the perpendicular bisector to the line final line you got and the point where the bisector cuts the perpendicular to the base is the third vertex of the triangle.

Complete step-by-step answer:
Let us start the construction by drawing the base of length 12 cm and marking the end points as A and B.

Now draw a line perpendicular to AB from point A and mark a point 18cm from the point A on the perpendicular. For drawing the perpendicular bisector, a semicircle with radius at A and of any radius less than 12cm. Now keep a scale along the line AB and mark the point where the line AB extended would meet the semi-circle. Take a compass and place on the point and extend the hands so that the radius is equal to the distance between the two meeting points of the semi-circle and the base. Draw arcs from the two meet points and draw the line passing through the meet point of the arc and point A to get the perpendicular from point A.

Now join the points H and B and draw a perpendicular bisector to the line HB so that it meets the segment AH at point C. For drawing the perpendicular bisector, take a compass and extend its hands more than half of HB. Now, draw arc with centre H and B, the arcs meet at two different points on either sides of the line HB. Join the two points to get the perpendicular bisector.

The triangle ABC is the final right angled triangle that we were asked to construct. So, now have a look at the final clear picture we get:

Note: If we want we can solve the above question by first using the Pythagoras theorem to find the lengths of hypotenuse and perpendicular separately and use the lengths to draw a triangle using a ruler, but that won’t be considered a proper construction for the question asked to us. In questions related to construction, try to avoid manual calculations as much as possible.