Question

Find the exact length of the floor clearance, using metres.

Answer 1

the length of the floor clearance is 2.8 m

Step-by-step explanation

as we have 2 similar triangles ( ABC and AED) we can set a proportion

Step 1

a)let

`ratio=\frac{vertical\text{ side}}{horizontal\text{ side}}`

so

for triangle ABC ( divide the given measure by 100 to obtain meters)

`ratio_1=\frac{0.30\text{ m}}{0.40\text{ m}}=(3)/(4)`

and

for triangle AED

let

`ratio_2=\frac{2.1}{floor\text{ clearance}}`

Step 2

as the ratio is the same, set the proportion

`\begin{gathered} ratio_1=ratio_2 \\ (3)/(4)=\frac{2.1}{floor\text{ clerance}} \\ solve\text{ for floor clearance} \\ floor\text{ }cleareance=(2.1*4)/(3) \\ floor\text{ }cleareance=2.8\text{ m} \end{gathered}`

therefore, the length of the floor clearance is 2.8 m

I hope this helps you