The height of the building is 200 feet
Solving linear equation mean calculating the unknown variable from the equation.
Let the linear equation : y = mx + c
If we draw the above equation on Cartesian Coordinates , it will be a straight line with :
m → gradient of the line
( 0 , c ) → y - intercept
Gradient of the line could also be calculated from two arbitrary points on line ( x₁ , y₁ ) and ( x₂ , y₂ ) with the formula :
[tex]\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}} }[/tex]
If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :
[tex]\large {\boxed {y - y_1 = m ( x - x_1 )} }[/tex]
Let us tackle the problem.
This probem is about Directly Proportionality.
Given :
Length of Building's shadow = s₁ = 48 feet
Length of Flagpole's shadow = s₂ = 9.6 feet
Height of Flagpole = h₂ = 40 feet
Unknown :
Height of Building = h₁ = ?
Solution :
Because length of shadow is directly proportional to the height of the object , then :
[tex]s_1 : s_2 = h_1 : h_2[/tex]
[tex]48 : 9.6 = h_1 : 40[/tex]
[tex]h_1 = \frac{48}{9.6} \times 40[/tex]
[tex]\large {\boxed {h_1 = 200 ~ \text{feet}} }[/tex]
Grade: High School
Subject: Mathematics
Chapter: Linear Equations
Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point
The height of the building will be 200 feet long.
Similar figures are those figures which are identical in shape, but not necessarily in size.
Two squares with sides of 10 and 5 are similar because their shape is exact but the size is different.
Another example is all circles are similar circles.
The ratio of corresponding sides of similar objects is always the same.
Given,
Shadow of building = 48 feet
Shadow of flagpole = 9.6 feet
Length of flagpole = 40 feet
Let's say
Length of building = x
Then
By similarity rule
x/48 = 40/9.6
x = 200 feet.
Hence, the height of the building will be 200 feet long.
To learn more about similarity,
https://brainly.com/question/23620710
#SPJ2
