Question

An acute triangle has side lengths 21 cm, x cm, and 2x cm. If 21 is one of the shorter sides of the triangle, what is the greatest possible length of the longest side, rounded to the nearest tenth?
18.8 cm
24.2 cm
42.0 cm
72.7 cm

Answer 1

Answer:

B. 24.2 cm

Step-by-step explanation:

We are given that,

Lengths of the sides of a triangle are 21 cm, x cm and 2x cm.

Using Triangle Inequality Theorem, which states that,

'The sum of measure of any two sides must be greater than the measure of the third side'.

Since, 21 cm is the shorter side. We have,

A)  $21+x>2x$     i.e.    $21>x$      or    $x$.

B)  $x+2x>21$     i.e.    $3x>21$    or    $x>7$

So, $7$

That is, $14$

Thus, the length of the larger side has measure between 14 cm and 42 cm.

Hence, the possible length of the longest side is 24.2 cm.

Answer 2

we know that

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side

so

case a) $21+x > 2x$

$21+x > 2x\\21> 2x-x\\21> x\\x < 21\ cm$

case b) $x+2x > 21$

$x+2x > 21\\3x> 21\\x> 7\ cm$

therefore

the longest side is $2x$

$x < 21\ cm\\2x < 42\ cm$

the longest side could be $41.99\ cm$

rounded to the nearest tenth is  $42\ cm$

the answer is the option

$42\ cm$