Question

A landscaper wants to create a 12-foot-long diagonal path through a rectangular garden. The width of the garden is x feet and the length of the garden is 4 more than the width.

Answer 1

Answer:

Width of the rectangle =  6.7 ft

length of the rectangle = 10.7 ft

Step-by-step explanation:

ABCD is the rectangle.

AB = length of the rectangle = 4 + x ft

BC = width of the rectangle = x ft

AC = Diagonal of the rectangular field = 12 ft

Since ΔABC is the Right angle triangle. So

$AC^{2} = AB^{2} + BC^{2}$

$12^{2} = (4 + x)^{2} + x^{2}$

$144 = x^{2} + 16 + x^{2} + 8 x$

$144 = 2x^{2} + 8x + 16$

$x^{2} + 4x -72 = 0$

By solving above equation we get

x = 6.7 ft

Thus is the width of the rectangle.

And length of the rectangle = 4 + x

⇒ 4 + 6.7

⇒ 10.7 ft

Answer 2

Answer:

6.2ft by 10.2ft :))

Step-by-step explanation: