The shorter sides of an acute triangle are x cm and 2x cm. the longest side of the triangle is 15 cm. what is the smallest possible whole-number value of x? a. 6 b. 7 c. 8 d. 9

Correct choice is B

Step-by-step explanation:

A triangle can be formed with three segments of lengths a, b and c if

If the shorter sides of an acute triangle are x cm and 2x cm, then

Thus,

You get possible values for x:

If triangle is acute, then by the cosine law

The smallest possible whole-number value of x is 7.

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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.