A tree casts a shadow that is 9 meters long. A 54 meter tall building nearby casts a shadow that is 24 meters long. What is the height of the tree

Height of the tree is 20.25 m.

Step-by-step explanation:

Length of building AB = 54 m

Length of tree DE = 9 m

Shadow casted by the building (BC) = 24 m

Shadow casted by the tree (CE) = 9 m

Since, ΔABC ~ ΔDEC

By the property of similar triangles, corresponding sides of the similar triangles will be proportional.

h =

h = 20.25 m

Therefore, height of the tree is 20.25 m.

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is