Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. What will be the length (longer dimension) of the new garden? Enter your answer in the box.

Step-by-step explanation:

Let x represent the constant amount by which the length and width of the garden is increased.

Tyler has a rectangular garden that measures 10 m wide by 13 m long. He wants to increase the area to 208 m² by increasing the width and length by the same amount. This means that the new length of the garden would be (13 + 2x) cm and the new width of the garden would be (10 + 2x) cm. Therefore,

(13 + 2x)(10 + 2x) = 208

130 + 26x + 20x + 4x² -208 = 0

4x² + 46x - 208 - 130 = 0

4x² + 46x - 78 = 0

Dividing through by 2, it becomes

2x² + 23x - 39 = 0

2x² + 26x - 3x - 39 = 0

2x(x + 13) - 3(x + 13) = 0

2x - 3 = 0 or x + 13 = 0

x = 3/2 or x = - 13

Since the value of x cannot be negative, then

x = 3/2 = 1.5 m

The length of the new garden is

13 + 1.5 = 14.5 m

x

step-by-step explanation:

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