RD Sharma 2020 solution class 9 chapter 16 Construction Exercise 16.3

Exercise 16.3

Page-16.18

Question 1:

Construct a Δ ABC in which BC = 3.6 cm, AB + AC = 4.8 cm and ∠B = 60°.

Answer 1:

We are asked to construct a triangle ABC in which, and

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of 3.6 cm

STEP2: Draw.

STEP3: From ray BE, cut BD of 4.8 cm.

STEP4: Draw segment DC.

STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A

STEP6: Draw segment AC.

ΔABC is the required angle.

Question 2:

Construct a Δ ABC in which AB + AC = 5.6 cm, BC = 4.5 cm and ∠B = 45°.

Answer 2:

We are asked to construct a triangle ABC in which, and

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of 4.5 cm.

STEP2: Draw

STEP3: From ray BE, cut BD of 5.6 cm.

STEP4: Draw segment DC.

STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A

STEP6: Draw segment AC.

ΔABC is the required angle.

Question 3:

Construct a Δ ABC in which BC = 3.4 cm, AB − AC = 1.5 cm and ∠B = 45°.

Answer 3:

We are asked to construct a triangle ABC in which , and

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of 3.4 cm.

STEP2: Draw CBE =

STEP3: From the ray BE, cut BD of 1.5 cm.

STEP4: Draw segment DC.

STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at A

STEP6: Draw AC.

ΔABC is the required angle.

Question 4:

Using ruler and compasses only, construct a ΔABC, given base BC = 7 cm, ∠ABC = 60° and AB + AC = 12 cm.

Answer 4:

We are asked to construct a triangle ABC in which BC = 7 cm, ∠B = 60° and AB  + AC = 12 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw BC of length 7 cm.

STEP2: With B as a centre, and convenient radius draw an arc cutting BC at N.

STEP3: With N as a centre, and same radius draw an arc cutting the previous arc at M.

STEP4: Draw BM and produce it to P.

STEP5: From BP, cut BR = 12 cm.

STEP6: Draw segment RC.

STEP7: Draw perpendicular bisector of RC. It cuts the ray BR at A.

STEP8: Draw AC.

ΔABC is the required triangle.

Question 5:

Construct a right-angled triangle whose perimeter is equal to 10 cm and one acute angle equal to 60°.

Answer 5:

We are asked to draw triangle ABC whose base angles are 60$°$ and 90$°$ and its perimeter is 10 cm.

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw a line segment DE of 10 cm.

STEP2: Draw ∠EDM = ∠B = 90° and ∠DEN = ∠C = 60°.

STEP3: Draw the angle bisectors of ∠EDM and ∠DEN and mark their point of intersection as A.

STEP4: Draw the perpendicular bisectors of AD and AE. They meet DE at B and C respectively.

STEP5: Draw AB and AC to get the desired ΔABC.

Question 6:

Construct a triangle ABC such that BC = 6 cm, AB = 6 cm and median AD = 4 cm.

Answer 6:

We are given and median

We have to construct the triangle ABC

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw a line segment BC of length 6 cm.

STEP2: Draw the perpendicular bisector of line BC cutting the line at point D, such that BD = 3 cm.

STEP3: With centre B and radius = 6 cm, draw an arc.

STEP4: With centre D and radius = 4 cm, draw an arc intersecting the previous arc at A.

STEP5: Draw AC to get the desired ΔABC.

Question 7:

Construct a right triangle ABC whose base BC is 6 cm and the sum of hypotenuse AC and other side AB is 10 cm.

Answer 7:

We have to construct a right triangle ABC with base and the sum of hypotenuse and the other side is 10 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw a line segment BC of length 6 cm.

STEP2: Draw CBE =

STEP3: From BE, cut BD of length 10 cm.

STEP4: Draw the line segment DC.

STEP5: Draw the perpendicular bisector of DC, intersecting the ray BE at point A

STEP6: Draw AC to get the desired ΔABC.

Question 8:

Construct a triangle whose perimeter is 6.4 cm, and angles at the base are 60° and 45°.

Answer 8:

We are asked to draw triangle ABC whose base angles are 60° and 45° and its perimeter is 6.4 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw DE of 6.4 cm.

STEP2: Draw ∠EDP =∠B = 60° and ∠DER = ∠C = 45°.

STEP3: Draw the angle bisectors of ∠EDP and ∠DER and mark their point of intersection as A.

STEP4: Draw the perpendicular bisectors of AD and AE. They meet DE at point B and Point C respectively.

STEP5: Draw AB and AC to get the required ΔABC.

Question 9:

Using ruler and compasses only, construct a Δ ABC from the following data:
AB + BC + CA = 12 cm, ∠B = 45° and ∠C = 60°.

Answer 9:

We are asked to draw triangle ABC whose base angles are 60° and 45° and its perimeter is 12 cm

We will follow the following algorithm for the construction

Steps of construction

STEP1: Draw DE of length 12 cm.

STEP2: Construct ∠EDP =∠C = 60° and ∠DER =∠B = 45°, using regular methods.

STEP3: Draw the angle bisectors of ∠EDP and ∠DER and mark their point of intersection as A.

STEP4: Draw the perpendicular bisectors of AE and AD. They meet DE at point B and Point C respectively.

STEP5: Draw AB and AC to get the required ΔABC.

Question 10:

Construct a triangle XYZ in which ∠Y = 30°, ∠Z = 90° and XY + YZ + ZX = 11.

Answer 10:

We are asked to construct a triangle XYZ such that

We will follow the following algorithm for the construction

Steps of construction-

STEP1: Draw a line segment AB of length 11 cm.

STEP2: Draw BAC = Y = and ABD =Z =

STEP3: Bisect BAC and ABD and mark the point of intersection of these angle bisectors by X.

STEP4: Draw perpendicular bisectors of AX and XB. They meet AB at point Y and Z, respectively.

STEP5: Draw XY and XZ to get the desired ΔXYZ.