60 cm2 w + 4 54. Area ofa Rectangle. The length of a rectangle is 3 m greater th
ID: 3138918 • Letter: 6
Question
60 cm2 w + 4 54. Area ofa Rectangle. The length of a rectangle is 3 m greater than the width. The area is 70 m2. Find the length and the width. 55. Plumbing. A pipe runs diagonally under a rectan gular yard that is 6 m longer than it is wide. If the pipe is 30 m long, determine the dimensions of the yard. 56. Guy Wires. A 26-ft long guy wire is anchored 10 ft from the base of a telephone pole. How far up the pole does the wire reach? 57. Right Triangles. The area of a right triangle is 26 cm2. One leg is 5 cm shorter than the other. Find the lengths of the legs. 58. Right Triangles. The area of a right triangle is 31 m2. One leg is 2.4 m shorter than the other. Find the lengths of the legs. 59. Area ofa Rectangle. The length of a rectangle is 5 ft greater than the width. The area is 25 ft. Find the length and the width. 60. Area of a Rectangle. The length of a rectangle is 3 in. greater than the width. The area is 30 in?. FindExplanation / Answer
54. Let the width of the rectangle be w meters. Then its length is w+3 meters so that its area is length*width = (w+3)w = w2+3w = 70. Then w2+3w-70= 0 or, w2+10w-7w-70= 0 or, w(w+10)-7(w+10)= 0 or, (w-7)(w+10) = 0. Therefore, w = -10 or, w = 7. However, since w cannot be negative, we have w = 7. Thus, the width and the length of the rectangle are 7meters and 10 meters respectively.
55. Let the width of the rectangular yard be w meters. Then its length is w+6 meters so that, as per Pythagoras theorem, ?[w2+(w+6)2] = 30 or, w2+(w+6)2 =900 or, 2w2+12w+36 = 900 or, 2w2+12w-864 = 0 or, w2+6w-432 = 0. On using the quadratic formula, we have w = [-6 ±?( 36+4*432)]/2 = (-6±?1764)/2= (-6±42)/2 = (42-6)/2 = 36/2 = 18 ( as w cannot be negative).Thus, the width and the length of the rectangular yard are 18 meters and 24 meters respectively).
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