The lengths of the sides of a quadrilateral are 4 consecutive even integers. The perimeter of the quadrilateral is 36 inches. What is the length of the longest side?

Length of longest side is 10.5 inches

Step-by-step explanation:

Let the shortest side of the quadrilateral be x inches

The length of the consecutive sides will be;

x , x + 1 , x + 2 and x + 3 inches

By adding all

together, we get the perimeter of the quadrilateral

so;

x + x + 1 + x + 2 + x + 3 = 36

4x + 6 = 36

4x = 36-6

4x = 30

x = 30/4

x = 7.5 inches

The longest side is x + 3 = 7.5 + 3 = 10.5 inches

part a: triangles gcb and epb

part b. sides cg and rp are parallel by definition of parallelogram.

angles cgb and e are congruent by being alternate interior angles of parallel lines cut by a transversal. angles gbc and ebp are congruent because they are vertical angles. by aa similarity, the triangles are similar.

part c. since the triangles are similar, the ratios of the lengths of corresponding sides are equal.

calculation of be:

gb/be = cb/bp

(400 ft)/be = 300/200

(400 ft)/be = 3/2

3be = 2 * 400 ft

3be = 800 ft

be = 800/3 ft

calculation of pe:

gc/pe = cb/bp

(350 ft)/pe = 300/200

(350 ft)/pe = 3/2

3pe = 2 * 350 ft

3pe = 700 ft

pe = 700/3 ft

the correct answer would be d because the slope is -2/2=1 and the y intercept is at 2 so that is the correction equation