N A rectangular patio has an area of 2x2 + 13x − 24 ft2. Use factoring to find
possible dimensions of the patio. The patio is
to be enlarged so that each dimension is 2 ft
greater than it was originally. What are the
new dimensions of the patio? What is the new
area of the patio?

no this is a nonlinear negative

=

x=0.8898305 is the answer to that equation

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