the area of the green square is 9 ft2. the area of the yellow square is 25 ft2.
what is the area of the red square (labelled "b" in the diagram)?

area = 16 ft²

Step-by-step explanation:

The area of the green square = 9 ft²

area of the yellow square = 25 ft²

Area of the red square can be computed as follows:

area of a square = L²

Since one side of each triangle forms a part of the triangle knowing the length of sides of the green and yellow triangle can be use to get the sides of the red square and invariably the area.

Green square

L² = 9

square both sides

√L² = √9

L = 3 ft

Yellow square

L² = 25

square both sides

√L² = √25

L = 5 ft

use Pythagoras theorem to get the third side of the triangle which is the b

c² = a² + b²

b² = c²  - a²

a = 3 ft

c = 5 ft

b² =  5² - 3²

b² = 25 - 9

b² = 16

square both sides

√b² = √16

b = 4

Red square

area = L²

area = 4²

area = 16 ft²

mx+89b(-98)nb

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true