Question

What is the value of m In the figure below in this diagram

Answer 1

(A)
`√(126)`

Explanation:

Since, it is given that ΔABD is similar to ΔBCD, then

`(AB)/(BC)=(BD)/(CD)=(AD)/(BD)`

`(AB)/(m)=(BD)/(7)=(11)/(BD)`

Taking second and third equality, we get

`(BD)^(2)=77`

⇒
`BD=√(77)`

Now, from ΔBDC, using the Pythagoras theorem, we get

`(BC)^(2)=(BD)^(2)+(DC)^2`

`m^(2)=(7)^2+(√(77))^2`

`m^2=49+77`

`m^2=126`

`m=√(126)`.

Answer 2

Since
`\triangle ABD\sim \triangle BCD,` the corresponding sides are proportional:

`(AB)/(BC)=(BD)/(CD)=(AD)/(BD).`

You are given that

• 
  `BC=m;`
• 
  `DC=7;`
• 
  `AD=11.`

Thus,

`(AB)/(m)=(BD)/(7)=(11)/(BD).`

From the second equality
`(BD)/(7)=(11)/(BD)` you have that

`BD^2=7\cdot 11=77,\\ \\BD=√(77).`

Now consider right triangle BDC (with right angle D). By the Pythagorean theorem,

`BC^2=BD^2+DC^2,\\ \\m^2=(√(77))^2+7^2=77+49=126,\\ \\m=√(126).`

Answer: correct choice is A.