Question

A building casts a shadow 48 feet long. At the same time, a 40 foot tall flagpole cast a shadow 9.6 feet long. What is the height of the building

Answer 1

X is the variable used in place of the building's height. I apologize if you can't read my hand writing very well.

Answer 2

The height of the building is 200 feet

Further explanation

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 :

$\large {\boxed {m = \frac{y_2 - y_1}{x_2 - x_1}} }$

If point ( x₁ , y₁ ) is on the line with gradient m , the equation of the line will be :

$\large {\boxed {y - y_1 = m ( x - x_1 )} }$

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 :

$s_1 : s_2 = h_1 : h_2$

$48 : 9.6 = h_1 : 40$

$h_1 = \frac{48}{9.6} \times 40$

$\large {\boxed {h_1 = 200 ~ \text{feet}} }$

Learn more

• Infinite Number of Solutions : brainly.com/question/5450548
• System of Equations : brainly.com/question/1995493
• System of Linear equations : brainly.com/question/3291576

Answer details

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

Keywords: Linear , Equations , 1 , Variable , Line , Gradient , Point