Give a Teacher's Solution using algebra for the following problem: The Lengths of the sides of a triangle, measured in inches, are consecutive whole
numbers, and the perimeter is 27 inches. What is the length of the longest side?

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.

c-   36

taxicab circle radius 9 has 4(9) = 36 points