RD Sharma Solutions: Constructions (Exercise 17.5)

 Page 1


  
 
 
 
  
 
 
 
        
 
1. Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm. 
 
Solution: 
 
Steps of construction: 
 1. Draw a line segment QR = 4 cm. 
 2. Draw ?QRX of measure 90
o
. 
 3. With center Q and radius PQ = 5 cm, draw an arc of the triangle to intersect ray RX at 
P. 
 4. Join PQ to obtain the desired triangle PQR. 
 5. PQR is the required triangle.   
 
2. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 
2.5 cm. 
 
Solution: 
Page 2


  
 
 
 
  
 
 
 
        
 
1. Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm. 
 
Solution: 
 
Steps of construction: 
 1. Draw a line segment QR = 4 cm. 
 2. Draw ?QRX of measure 90
o
. 
 3. With center Q and radius PQ = 5 cm, draw an arc of the triangle to intersect ray RX at 
P. 
 4. Join PQ to obtain the desired triangle PQR. 
 5. PQR is the required triangle.   
 
2. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 
2.5 cm. 
 
Solution: 
  
 
 
 
  
 
 
 
 
Steps of construction: 
1. Draw a line segment QR = 2.5 cm. 
2. Draw ?QRX of measure 90
o
. 
3. With center Q and radius PQ = 4 cm, draw an arc of the triangle to intersect ray RX at 
P. 
4. Join PQ to obtain the desired triangle PQR. 
5. PQR is the required triangle. 
 
3. Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute 
angles of measure 30
o 
 
Solution: 
 
Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let C = 30
o
. 
Therefore ?A + ?B + ?C = 180
o 
?B = 180
o 
- 30
o
- 90
o
 = 60
o 
Steps of construction: 
1. Draw a line segment BC = 5.4 cm. 
Page 3


  
 
 
 
  
 
 
 
        
 
1. Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm. 
 
Solution: 
 
Steps of construction: 
 1. Draw a line segment QR = 4 cm. 
 2. Draw ?QRX of measure 90
o
. 
 3. With center Q and radius PQ = 5 cm, draw an arc of the triangle to intersect ray RX at 
P. 
 4. Join PQ to obtain the desired triangle PQR. 
 5. PQR is the required triangle.   
 
2. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 
2.5 cm. 
 
Solution: 
  
 
 
 
  
 
 
 
 
Steps of construction: 
1. Draw a line segment QR = 2.5 cm. 
2. Draw ?QRX of measure 90
o
. 
3. With center Q and radius PQ = 4 cm, draw an arc of the triangle to intersect ray RX at 
P. 
4. Join PQ to obtain the desired triangle PQR. 
5. PQR is the required triangle. 
 
3. Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute 
angles of measure 30
o 
 
Solution: 
 
Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let C = 30
o
. 
Therefore ?A + ?B + ?C = 180
o 
?B = 180
o 
- 30
o
- 90
o
 = 60
o 
Steps of construction: 
1. Draw a line segment BC = 5.4 cm. 
  
 
 
 
  
 
 
 
2. Draw angle CBY = 60
o 
3. Draw angle BCX of measure 30
o
 with X on the same side of BC as Y. 
4. Let BY and CX intersects at A. 
5. Then ABC is the required triangle. 
 
 
4. Construct a right triangle ABC in which AB = 5.8 cm, BC = 4.5 cm and ?C = 90
o
. 
 
Solution: 
 
Steps of construction: 
1. Draw a line segment BC = 4.5 cm. 
2. Draw ?BCX of measure 90
o 
3. With center B and radius AB = 5.8 cm, draw an arc of the triangle to intersect ray CX 
at A. 
4. Join AB to obtain the desired triangle ABC. 
5. ABC is the required triangle. 
 
5. Construct a right triangle, right angled at C in which AB = 5.2 cm and BC= 4.6 cm. 
 
Solution: 
Page 4


  
 
 
 
  
 
 
 
        
 
1. Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm. 
 
Solution: 
 
Steps of construction: 
 1. Draw a line segment QR = 4 cm. 
 2. Draw ?QRX of measure 90
o
. 
 3. With center Q and radius PQ = 5 cm, draw an arc of the triangle to intersect ray RX at 
P. 
 4. Join PQ to obtain the desired triangle PQR. 
 5. PQR is the required triangle.   
 
2. Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 
2.5 cm. 
 
Solution: 
  
 
 
 
  
 
 
 
 
Steps of construction: 
1. Draw a line segment QR = 2.5 cm. 
2. Draw ?QRX of measure 90
o
. 
3. With center Q and radius PQ = 4 cm, draw an arc of the triangle to intersect ray RX at 
P. 
4. Join PQ to obtain the desired triangle PQR. 
5. PQR is the required triangle. 
 
3. Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute 
angles of measure 30
o 
 
Solution: 
 
Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let C = 30
o
. 
Therefore ?A + ?B + ?C = 180
o 
?B = 180
o 
- 30
o
- 90
o
 = 60
o 
Steps of construction: 
1. Draw a line segment BC = 5.4 cm. 
  
 
 
 
  
 
 
 
2. Draw angle CBY = 60
o 
3. Draw angle BCX of measure 30
o
 with X on the same side of BC as Y. 
4. Let BY and CX intersects at A. 
5. Then ABC is the required triangle. 
 
 
4. Construct a right triangle ABC in which AB = 5.8 cm, BC = 4.5 cm and ?C = 90
o
. 
 
Solution: 
 
Steps of construction: 
1. Draw a line segment BC = 4.5 cm. 
2. Draw ?BCX of measure 90
o 
3. With center B and radius AB = 5.8 cm, draw an arc of the triangle to intersect ray CX 
at A. 
4. Join AB to obtain the desired triangle ABC. 
5. ABC is the required triangle. 
 
5. Construct a right triangle, right angled at C in which AB = 5.2 cm and BC= 4.6 cm. 
 
Solution: 
  
 
 
 
  
 
 
 
 
Steps of construction: 
1. Draw a line segment BC = 4.6 cm. 
2. Draw ?BCX of measure 90
o 
3. With center B and radius AB = 5.2 cm, draw an arc of the triangle to intersects ray CX 
at A. 
4. Join AB to obtain the desired triangle ABC. 
5. ABC is the required triangle.