In this exercise, we shall discuss the RHS triangle construction and the steps involved in them. The primary objective is to help students improve their problem-solving abilities, which in turn, helps in boosting their confidence level to achieve high marks in their exams. Students can refer to and download RD Sharma Solutions for Class 7 Maths Exercise 17.5 Chapter 17 Constructions. These solutions are formulated by BYJU’S subject experts in Maths.

RD Sharma Solutions for Class 7 Maths Chapter 17 – Constructions Exercise 17.5

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Access answers to Maths RD Sharma Solutions for Class 7 Chapter 17 – Constructions Exercise 17.5

Exercise 17.5 Page No: 16.3

1. Draw a right triangle with a 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 centre 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 centre 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 centre 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 centre 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.