sat suite question viewer

Geometry and Trigonometry Difficulty: Hard

A rectangular poster has an area of $360$ square inches. A copy of the poster is made in which the length and width of the original poster are each increased by $20 percent sign$ . What is the area of the copy, in square inches?

Back question 77 of 268 Next

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268

Explanation

The correct answer is $518.4$ . It's given that the area of the original poster is $360$ square inches. Let $l$ represent the length, in inches, of the original poster, and let $w$ represent the width, in inches, of the original poster. Since the area of a rectangle is equal to its length times its width, it follows that $360 equals script l w$ . It's also given that a copy of the poster is made in which the length and width of the original poster are each increased by $20 percent sign$ . It follows that the length of the copy is the length of the original poster plus $20 percent sign$ of the length of the original poster, which is equivalent to $l + \frac{20}{100} l$ inches. This length can be rewritten as $script l plus 0.2 script l$ inches, or $1.2 script l$ inches. Similarly, the width of the copy is the width of the original poster plus $20 percent sign$ of the width of the original poster, which is equivalent to $w + \frac{20}{100} w$ inches. This width can be rewritten as $w plus 0.2 w$ inches, or $1.2 w$ inches. Since the area of a rectangle is equal to its length times its width, it follows that the area, in square inches, of the copy is equal to $left parenthesis 1.2 script l right parenthesis left parenthesis 1.2 w right parenthesis$ , which can be rewritten as $left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis script l w right parenthesis$ . Since $360 equals script l w$ , the area, in square inches, of the copy can be found by substituting $360$ for $l w$ in the expression $left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis script l w right parenthesis$ , which yields $left parenthesis 1.2 right parenthesis left parenthesis 1.2 right parenthesis left parenthesis 360 right parenthesis$ , or $518.4$ . Therefore, the area of the copy, in square inches, is $518.4$ .