Question

What is the value of min the figure below?11mсO A. 336O B. 77O C. V178D. V624O E. 42F. 126

Answer 1

EXPLANATIONS:

We are given a right triangle labelled ABC. The sides indicated are;

`\begin{gathered} Shorter\text{ }leg=m \\ Hypotenuse=(11+7)=18 \end{gathered}`

Also extracted from this triangle we have a smaller right triangle labelled BDC. The sides are labeled;

`\begin{gathered} Shorter\text{ }leg=7 \\ Hypotenuse=m \end{gathered}`

We will begin by recalling the Pythagoras theorem which states;

`\begin{gathered} Pythagoras\text{ }Theorem: \\ c^2=a^2+b^2 \end{gathered}`

Where c is the hypotenuse and a and b are the other two legs.

We can find the ratio between both triangles, because they are both similar by virtue of sharing one common side, that is side BD.

Hence, we will have;

`\begin{gathered} For\text{ }\Delta ABC \\ BC=Shorter\text{ }leg \\ AC=Hypotenuse \\ For\text{ }\Delta BDC \\ DC=Shorter\text{ }leg \\ BC=Hypotenuse \end{gathered}`

We can now set up the following equation;

`(BC^2)/(AC^2)=(DC^2)/(BC^2)`

We now have;

`(m^2)/(18^2)=(7^2)/(m^2)`

We can cross multiply and we'll have;

`m^2* m^2=18^2*7^2`
`m^4=324*49`
`m^4=15876`

Next we take the square root of both sides;

`√(m^4)=√(15876)`
`m^2=126`

We take the square root of both sides yet again;

`√(m^2)=√(126)`
`m=√(126)`

ANSWER:

Option F is the correct answer.