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# Constructions Exercise 17.5

### Question: 1

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

### Solution: Steps of construction:

• Draw a line segment QR = 4 cm.

• Draw ∠QRX of measure 90°.

• With centre Q and radius PQ = 5 cm, draw an arc of the circle to intersect ray RX at P.

• Join PQ to obtain the desired triangle PQR.

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.

### Solution: Steps of construction:

• Draw a line segment QR = 2.5 cm.

• Draw ∠QRX of measure 90°.

• With centre Q and radius PQ = 4 cm, draw an arc of the circle to intersect ray RX at P.

• Join PQ to obtain the desired triangle PQR.

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°

### Solution: Let ABC be the right triangle at A such that hypotenuse BC = 5.4 cm. Let cC = 30°.

Therefore ∠+ ∠+ ∠= 180°∠= 180°− 30°− 90° = 60°

Steps of construction:

• Draw a line segment BC = 5.4 cm.

• Draw angle CBY = 60°

• Draw angle BCX of measure 30° with X on the same side of BC as Y.

• 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 ∠= 90°.

### Solution: Steps of construction:

• Draw a line segment BC = 4.5 cm.

• Draw ∠BCX of measure 90°..

• With centre B and radius AB = 5.8 cm, draw an arc of the circle to intersect ray BX at A.

• Join AB to obtain the desired triangle ABC.

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.

### Solution: Steps of construction:

• Draw a line segment BC = 4.6 cm.

• Draw ∠BCX of measure 90°

• With centre B and radius AB = 5.2 cm, draw an arc of the circle to intersect ray CX at A.

• Join AB to obtain the desired triangle ABC.

ABC is the required triangle.