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My yard is 25 by 29 meters. I want a flower garden in the middle leaving a strip of grass of uniform width?

My yard is 25 by 29 meters. I want a flower garden in the middle leaving a strip of grass of uniform width around it. I must have 368m^2of grass. Under these conditions what will the length and width of the garden be.

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1. Draw a diagram. Draw a rectangle representing your yard. Indicate that lengths of the sides are 25 and 29. Draw a rectangle within this rectangle, representing the garden. Let x denote the width (in meters) of the strip of grass. Observe that the garden is (25 - 2x) by (29 - 2x). Extend the sides of the garden to meet the outer rectangle. This divides the grass into 8 regions: 4 squares that are x by x 2 rectangles that are (25 - 2x) by x 2 rectangles that are (29 - 2x) by x The total area A of these regions is given by A = 4x² + 2x(25 - 2x) + 2x(29 - 2x) which simplifies to A = -4x² + 108x Since you want A to equal 368 m², we must have 368 = -4x² + 108x 92 = -x² + 27x x² - 27x + 92 = 0 (x - 4)(x - 23) = 0 x = 4 or x = 23 The second solution is unphysical; it makes your garden -21 meters by -17 meters! So x = 4 meters, and your garden will be (25 - 2*4) by (29 - 2*4), or 17 by 21 meters.