RD Sharma solution class 7 chapter 17 Construction Exercise 17.5

Exercise 17.5

Pages-17.8

Question 1:

Draw a right triangle with hypotenuse of length 5 cm and one side of length 4 cm.

Answer 1:

Steps of construction:

1. Draw a line segment QR = 4 cm.
2. Draw $\angle$QRX of measure 90$°$.
3. With centre Q and radius PQ = 5 cm, draw an arc of the circle to intersect ray RX at P.
4. Join PQ to obtain the desired triangle PQR.
5. PQR is the required triangle.

                                                                                                                                  

Question 2:

Draw a right triangle whose hypotenuse is of length 4 cm and one side is of length 2.5 cm.

Answer 2:

Steps of construction:

1. Draw a line segment QR = 2.5 cm.
2. Draw $\angle$QRX of measure 90$°$.
3. With centre Q and radius PQ = 4 cm, draw an arc of the circle to intersect ray RX at P.
4. Join PQ to obtain the desired triangle PQR.
5. PQR is the required triangle.

 

Question 3:

Draw a right triangle having hypotenuse of length 5.4 cm, and one of the acute angles of measure 30°.

Answer 3:

Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let $\angle C = 30°$.
Therefore $$\begin{gathered} \angle A+\angle B+\angle C =180° \\ \angle B =180-30-90 = 60° \end{gathered}$$
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 intersect at A.

Then ABC is the required triangle.

Question 4:

Construct a right triangle ABC in which AB = 5.8 cm, BC = 4.5 cm and ∠C = 90°.

Answer 4:

Steps of construction:

1. Draw a line segment BC = 4.5 cm.
2. Draw $\angle$BCX of measure 90$°$.
3. With centre B and radius AB =5.8 cm, draw an arc of the circle to intersect ray BX at A.
4. Join AB to obtain the desired triangle ABC.
5. ABC is the required triangle.                                                

 

Question 5:

Construct a right triangle, right angled at C in which AB = 5.2 cm and BC = 4.6 cm.

Answer 5:

Steps of construction:

1. Draw a line segment BC = 4.6 cm.
2. Draw $\angle$BCX of measure 90$°$.
3. With centre B and radius AB = 5.2 cm, draw an arc of the circle to intersect ray CX at A.
4. Join AB to obtain the desired triangle ABC.
5. ABC is the required triangle.