Question

You are 6 feet tall and cast an 8-foot shadow. A lamppost nearby casts a shadow that is 13.5 feet. Which equation can you use to solve for the height (h) of the lamppost?

Answer 1

6/8 =x/13.5 You cross multiply. So X*8 = 8X and 6*13.5 = 81. 8X = 81 You divide both sides by 8 and your answer is x=10.125 feet

Answer 2

Equation to solve for the height:

`\displaystyle (h)/(13)=(6)/(8)`

Height of the lamppost: 9.75 ft

Explanation:

See the attached sketch of the situation. Notice it has to do with similar triangles.

Notice we set h to be the unknown height of the lamppost. The ratio of your height to your shadow is the same ratio as the lamppost height to its shadow, since they are proportional. In math that is the following equation:

`\displaystyle (h)/(13)=(6)/(8)`

You did not ask for the solution but for the equation but we can easily solve it by multiplying both sides by 13 and then simplify the resulting fraction, to get:

`\displaystyle h=(6\cdot13)/(8)=(39)/(4)=9.75`

So, the height of the lamppost is 9.75 ft