Sara is working on a geometry problem in her algebra class. the problem requires sara to use the two quadrilaterals below to answer a list of questions. part a: for what one value of x are the perimeters of the quadrilaterals the same? (hint: the perimeter of a quadrilateral is the sum of its sides.) part b: for what one value of x are the areas of the quadrilaterals the same? (hint: the area of a quadrilateral is the product of its base and height.)

Part A:

Given a square with sides 6 and x + 4. Also, given a rectangle with sides 2 and 3x + 4

The perimeter of the square is given by 4(x + 4) = 4x + 16

The area of the rectangle is given by 2(2) + 2(3x + 4) = 4 + 6x + 8 = 6x + 12

For the perimeters to be the same

4x + 16 = 6x + 12
4x - 6x = 12 - 16
-2x = -4
x = -4 / -2 = 2

The value of x that makes the perimeters of the quadrilaterals the same is 2.

Part B:

The area of the square is given by



The area of the rectangle is given by 2(3x + 4) = 6x + 8

For the areas to be the same



Thus, there is no real value of x for which the area of the quadrilaterals will be the same.