Can you compare the ratio of this reciprocal with the earlier one? Find each side of a figure given below, if its area is 64 cm2. Understand and Explore the problem • What information is given in the question? AB = BC = DC = AD, and ∠A = ∠B = ∠C = ∠D = 90° Hence ABCD is a square. • What are you trying to find? The value of one of the sides of the square ABCD. • Is there any information that is not needed? No. Make a Plan • In a square all sides are equal, therefore, square of a side gives the area. Solve (Side)2 = Area ⇒ (x + 2)2 = 64 ⇒ (x + 2)2 = 82 ⇒ x+2 =8 ⇒ x=8–2 ∴ x=6 ∴ Side = x + 2 = 6 + 2 = 8 cm Revise • The above answer is verified by squaring the side and comparing the result with the given area. ∴ (Side)2 = 82 = 64 = given area. To become familiar with some of the vocabulary terms in the chapter, consider the following: 1. The word equivalent contains the same root as the word equal. What do you think equivalent expressions are? 2. The word simplify means make less complicated. What do you think it means to simplify an expression?
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(b)