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

Solution:

Steps of Construction:

i) Draw the base BC = 12.

ii) At point B, make an angle CBX = 90°using a protractor.

iii) Cut a line segment BD = 18 cm on the ray BX using a compass.

iv) Join DC.

v) With D and C as the centers and radius greater than half of DC, draw arcs on either side of the line to intersect each other. Join the intersecting points and extend the perpendicular bisector of CD to meet BD at A.

vi) Join A and C.

ABC is the required right-angled triangle.

Verification:

On measuring we see that,

BC = 12cm, ∠B = 90 degrees, AB + 18 = 18cm.

☛ Check: Class 9 Maths NCERT Solutions Chapter 11

Video Solution:

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

Class 9 Maths NCERT Solutions Chapter 11 Exercise 11.2 Question 5

Summary:

It is given that we have to construct a right triangle whose base is 12 cm, and the sum of its hypotenuse and other side is 18 cm. We have drawn the triangle using a compass and ruler and justified the construction.

☛ Related Questions:

• Construct a triangle ABC in which BC = 7 cm, ∠B = 75° and AB + AC = 13 cm.
• Construct a triangle ABC in which BC = 8cm, ∠B = 45° and AB - AC = 3.5 cm
• Construct a triangle PQR in which QR = 6cm, Q = ∠60° and PR - PQ = 2cm.
• Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11 cm.