Given two line segments of lengths 7.5 cm and 4.6 cm respectively. Construct line segments. (i) of length equal to the sum of the lengths of (ii) of length equal to the difference of the lengths of Verify these lengths by measurements.

Question

KnowledgeBoat · Accepted Answer

Steps: 1. Draw a line segment AB = 7.5 cm and a line segment CD = 4.6 cm using ruler and compass. (i) Construction of PQ = AB + CD: 1. Draw any line l and mark a point P on it. 2. With the compass, take the length of AB (= 7.5 cm). Place the pointer at P and draw an arc cutting line l at point R. So, PR = AB = 7.5 cm. 3. Now, with the compass, take the length of CD (= 4.6 cm). Place the pointer at R and draw an arc cutting line l at point Q. So, RQ = CD = 4.6 cm. Thus, PQ = PR + RQ = 7.5 cm + 4.6 cm = 12.1 cm. On measuring PQ with a ruler, we find PQ = 12.1 cm. Hence, the length of = 12.1 cm. (ii) Construction of XY = AB CD: 1. Draw any line m and mark a point Z on it. 2. With the compass, take the length of AB (= 7.5 cm). Place the pointer at Z and draw an arc cutting line m at point Y. So, ZY = AB = 7.5 cm. 3. Now, with the compass, take the length of CD (= 4.6 cm). Place the pointer at Z and draw an arc cutting ZY at point X. So, ZX = CD = 4.6 cm. Thus, XY = ZY XZ = 7.5 cm 4.6 cm = 2.9 cm. On measuring XY with a ruler, we find XY = 2.9 cm. Hence, the length of XY = 2.9 cm.

Mathematics

Given two line segments of lengths 7.5 cm and 4.6 cm respectively. Construct line segments. (i) of length equal to the sum of the lengths of (ii) of length equal to the difference of the lengths of Verify these lengths by measurements.

Constructions

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