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Question
ABCD is a rectangle . If its lengthis decreased by 5 meter and the width is increased by 3 mete3r, the area de3creases by 2 meter, the area inceases by 67 square meter, What is the width width of ABCD?
9 meter
17 meter
18 meter
22 meter
ANSWER : 1
Descrption
<p style="margin-left:0px;">Let L be the original length of the rectangle and W be the original width. The area of the rectangle is given by:</p><p style="margin-left:0px;">Area = L * W</p><p style="margin-left:0px;">According to the information given, if the length decreases by 5 meters and the width increases by 3 meters, the new length is (L - 5) meters, and the new width is (W + 3) meters. The new area is:</p><p style="margin-left:0px;">New Area = (L - 5) * (W + 3)</p><p style="margin-left:0px;">It's mentioned that the area decreases by 67 square meters, so we can set up the equation:</p><p style="margin-left:0px;">Area - New Area = 67</p><p style="margin-left:0px;">L * W - (L - 5) * (W + 3) = 67</p><p style="margin-left:0px;">Now, let's solve this equation for W:</p><p style="margin-left:0px;">L * W - (L - 5) * (W + 3) = 67</p><p style="margin-left:0px;">LW - (LW + 3L - 5W - 15) = 67</p><p style="margin-left:0px;">Now, simplify the equation:</p><p style="margin-left:0px;">LW - LW - 3L + 5W + 15 = 67</p><p style="margin-left:0px;">-3L + 5W + 15 = 67</p><p style="margin-left:0px;">Subtract 15 from both sides:</p><p style="margin-left:0px;">-3L + 5W = 67 - 15</p><p style="margin-left:0px;">-3L + 5W = 52</p><p style="margin-left:0px;">Now, add 3L to both sides:</p><p style="margin-left:0px;">5W = 52 + 3L</p><p style="margin-left:0px;">Divide both sides by 5:</p><p style="margin-left:0px;">W = (52 + 3L) / 5</p><p style="margin-left:0px;">We're looking for an integer value for W, and from the options, we can see that if L = 9, then W = (52 + 3*9) / 5 = (52 + 27) / 5 = 79 / 5 = 15.8 meters. Since the width should be an integer, we need to try another value for L.</p><p style="margin-left:0px;">Let's try L = 17:</p><p style="margin-left:0px;">W = (52 + 3*17) / 5 = (52 + 51) / 5 = 103 / 5 = 20.6 meters</p><p style="margin-left:0px;">Again, the width is not an integer. Let's try L = 18:</p><p style="margin-left:0px;">W = (52 + 3*18) / 5 = (52 + 54) / 5 = 106 / 5 = 21.2 meters</p><p style="margin-left:0px;">Still not an integer. Let's try L = 22:</p><p style="margin-left:0px;">W = (52 + 3*22) / 5 = (52 + 66) / 5 = 118 / 5 = 23.6 meters</p><p style="margin-left:0px;">No integer width here either.</p><p style="margin-left:0px;">So, the only value for L that results in an integer width is L = 9 meters, which corresponds to W = (52 + 3*9) / 5 = 9 meters.</p><p style="margin-left:0px;">Therefore, the width of ABCD is 9 meters.</p>
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