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 heigh

Question

4 years ago

13

t of the building

2 answers:

slavikrds [6] · Answer 1 · 2022-01-03T04:02:05+03:00

5 0

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

Shkiper50 [21] · Answer 2 · 2022-01-03T05:09:02+03:00

The height of the building is 200 feet

<h3>Further explanation</h3>

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 :

<em>m → gradient of the line</em>

<em>( 0 , c ) → y - intercept</em>

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.

<u>Given</u> :

Length of Building's shadow = s₁ = 48 feet

Length of Flagpole's shadow = s₂ = 9.6 feet

Height of Flagpole = h₂ = 40 feet

<u>Unknown :</u>

Height of Building = h₁ = ?

<u>Solution :</u>

Because length of shadow is directly proportional to the height of the object , then :

$s_1 : s_2 = h_1 : h_2$

$48 : 9.6 = h_1 : 40$

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

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

<h3>Learn more</h3>

<h3>Answer details</h3>

Grade: High School

Subject: Mathematics

Chapter: Linear Equations

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