Agardener has 46 feet of fencing to be used to enclose a rectangular garden that has a border of 2 feet wide surrounding it. if the length of the garden is to be twice the width, what will be the dimensions of the garden? what will be the area of the garden?

Imagine a rectangular area that represents the garden. Then, add a uniform margin of 2 ft around it. So, the length and width dimensions of the bigger outer rectangle would be added with 4 ft each, accounting for two 2-ft marginal distances on both ends. This would be the perimeter:

2(L+4) +2(W+4) = 46
Since L = 2W
2(2W +4) + 2(W+4) = 46
4W + 8 +2W + 8 = 46
W = 5 ft
L = 2(5) = 10 ft

Therefore, the dimensions of the garden is 10 ft in length and 5 ft in width. The area, consequently, is calculated as:

A = LW
A = (10 ft)(5 ft)
A = 50 ft²

Thus, the area of the garden is 50 ft².

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.