Part A: The area of a square is (16a2 − 24a + 9) square units. Determine the length of each side of the square by factoring the area expression completely. Show your work. (5 points) Part B: The area of a rectangle is (9a2 − 25b2) square units. Determine the dimensions of the rectangle by factoring the area expression completely. Show your work. (5 points) will give brainlist

Part A:

The area of a square is (16a2 − 24a + 9).

  16a2 − 24a + 9

= (4a)^2 - 2 x 4a x 3 + 3^2

= (4a - 3)^2

=> Side of square: 4a - 3 (if a > 4/3) or 3 - 4a (if a < 4/3)

Part B:

The area of a rectangle is (9a2 − 25b2).

  9a2 − 25b2

= (3a)^2 - (5b)^2

= (3a - 5b)(3a + 5b)

=> Side of rectangle: 3a - 5b and 3b + 5b

Hope this helps!

:)

Part A: 4a-3

Part B: (3a-5b) × (3a+5b)

Step-by-step explanation:

16a² - 24a + 9

(4a)² - 2(4a)(3) + 3²

(4a - 3)² = side²

side = 4a - 3

9a² - 25b²

(3a)² - (5b)²

(3a - 5b)(3a + 5b)

3/8

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