*The following problems were taken from the*

**GEOMETRY (COMMON CORE)**Regents Exam given on Thursday, January 26, 2017.Previous problems can be found here.

### Part 1

**7. The diagram below shows two similar triangles.
**

*If tan*~~O~~ = 3/7, what is the value of x, to the nearest tenth?(2) ** 5.6**.

tan

3x = (7)(2.4) = 16.8

x = 5.6

**8. A farmer has 64 feet of fence to enclose a rectangular vegetable garden. Which dimensions would result in the biggest area for this garden?
**

(1) *the length and the width are equal*

A dilation increased the size, so it will no longer be congruent.

For all rectangles with the same perimeter, a square will always have the greatest area.

Consider this:

A square with sides equal to x, will have a perimeter of 4x and area of x^{2}.

A rectangle with sides equal to (x+1) and (x-1), will have a perimeter of 4x and area of x^{2} - 1.

A rectangle with sides equal to (x+2) and (x-2), will have a perimeter of 4x and area of x^{2} - 4.

A rectangle with sides equal to (x+3) and (x-3), will have a perimeter of 4x and area of x^{2} - 9.

etc.

The area will always be some perfect subtracted from x^{2}, which will always be less than x^{2}.

Continue to the next problems.

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