SOLUTION: A rectangle was formed from a piece of wire whose length is 4m more than its width. The wire is bent again into a semi-circle with radius 17m, find the area of the rectangle.

Algebra ->  Rectangles -> SOLUTION: A rectangle was formed from a piece of wire whose length is 4m more than its width. The wire is bent again into a semi-circle with radius 17m, find the area of the rectangle.      Log On


   

Question 1186705: A rectangle was formed from a piece of wire whose length is 4m more than its
width. The wire is bent again into a semi-circle with radius 17m, find the area of the
rectangle.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Dimensions of rectangle
w+4 and w
Perimeter is 2%28w%2B4%29%2B2w=4w%2B4.
Rectangle's area is w%5E2%2B4w.

Semi-circle, radius 17 meters
Area is %281%2F2%29pi%2A17%5E2=%28289%2F2%29pi
Perimeter is %281%2F2%292pi%2A17%2B34=17pi%2B34


The two perimeters are equal in length.
4w%2B4=17pi%2B34
-
4w=17pi%2B30
highlight_green%28w=%2817pi%2B30%29%2F4%29---------width

highlight_green%28w%2B4=%2817pi%2B30%29%2F4%2B4%29---------length

You can multiply to get the area and simplify, or compute the value.

Answer by ikleyn(52779) About Me  (Show Source):
You can put this solution on YOUR website!
.

The meaning of this problem is unclear,

since it is unclear from the post, if the semi-circle includes the diameter, making the shape a closed curve.


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In distinction from other shapes, well defined in Geometry, like triangles, quadrilaterals, circles etc.,
semi-circle IS NOT a canonic well-defined shape (is not a canonical shape).

Therefore, when someone mentions a semi-circle, it should be described if the diameter is included or not.


Without clear meaning, the problem CAN NOT be solved, and any solution (as you obtained from the other tutor) is QUESTIONABLE.