A rectangle has a length of 15 less than 6 times its width. Find the length and width, if it has an area of 561 ?
x = width
6x - 15 = length {length is 15 less than 6 times the width}
Area of a rectangle = length x width
x(6x - 15) = 561 {multiplied width by length and set equal to area}
6x² - 15x = 561 {used distributive property}
6x² - 15x - 561 = 0 {subtracted 561 from each side}
2x² - 5x - 187 = 0 {divided entire equation by greatest common factor, 3}
Graph the equation using a graphing calculator or solve using the quadratic formula to find the x-intercept, which is solving the equation for x:
6x - 15 = length {length is 15 less than 6 times the width}
Area of a rectangle = length x width
x(6x - 15) = 561 {multiplied width by length and set equal to area}
6x² - 15x = 561 {used distributive property}
6x² - 15x - 561 = 0 {subtracted 561 from each side}
2x² - 5x - 187 = 0 {divided entire equation by greatest common factor, 3}
Graph the equation using a graphing calculator or solve using the quadratic formula to find the x-intercept, which is solving the equation for x:
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The x-intercepts are -8.5 and 11. Remember, x is the width of the rectangle, which cannot be negative. x = 11 {the width} 6x - 15 = 51 {the length} width = 11 length = 51 Ask the House |
