Find the fourth proportional to : (i) 4, 9, 32 (ii) 15, 6, 7 (iii) 0.6, 1.5, 3 (iv) (v) (vi) 3 hrs 12 min, 24 min, 1 m 68 cm

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KnowledgeBoat · Accepted Answer

(i) 4, 9, 32 Let the fourth proportional be x. Then 4, 9, 32, x are in proportion. product of extremes = product of means 4 × x = 9 × 32 ⇒ x = ⇒ x = 9 × 8 = 72 Hence, the fourth proportional is 72. (ii) 15, 6, 7 Let the fourth proportional be x. Then 15, 6, 7, x are in proportion. product of extremes = product of means 15 × x = 6 × 7 ⇒ x = Hence, the fourth proportional is 2.8 (iii) 0.6, 1.5, 3 Let the fourth proportional be x. Then 0.6, 1.5, 3, x are in proportion. product of extremes = product of means 0.6 × x = 1.5 × 3 ⇒ x = Hence, the fourth proportional is 7.5 (iv) Let the fourth proportional be x. Then , x are in proportion. product of extremes = product of means Hence, the fourth proportional is (v) Convert to improper fractions: . Let the fourth proportional be x. Then , x are in proportion. product of extremes = product of means Hence, the fourth proportional is 4 (vi) 3 hrs 12 min, 24 min, 1 m 68 cm First, convert to the same units for each ratio: 1 hour = 60 min, ∴ 3 hrs = 3 x 60 min = 180 min 3 hrs 12 min = 180 min + 12 min = 192 min. 1 m = 100 cm, ∴ 1 m 68 cm = 100 cm + 68 cm = 168 cm. Let the fourth proportional be x (in cm). We have: 192 : 24 :: 168 : x Then 192 min, 24 min, 168 cm, x are in proportion. product of extremes = product of means 192 x x = 24 x 168 ⇒ x = ⇒ x = ⇒ x = 21 Hence, the fourth proportional is 21 cm.

Mathematics

Find the fourth proportional to : (i) 4, 9, 32 (ii) 15, 6, 7 (iii) 0.6, 1.5, 3 (iv) (v) (vi) 3 hrs 12 min, 24 min, 1 m 68 cm

Ratio Proportion

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