Question

The lengths of two sides of a right triangle are 12 inches and 15 inches. What is the difference between the two possible lengths of the third side of the triangle? Round your answer to the nearest tenth. 10.2 inches 24.0 inches 28.2 inches 30.0 inches

Answer 1

Answer:

Option 1 - 10.2 inches.                            

Step-by-step explanation:

Given : The lengths of two sides of a right triangle are 12 inches and 15 inches.

To find : What is the difference between the two possible  lengths of the third side of the triangle?

Solution :

Since, It is a right angle triangle so we apply Pythagoras theorem,

$C^2=A^2+B^2$

Where, C is the hypotenuse the longer side of the triangle

A is the perpendicular

B is the base

There will be two cases,

1) Assume that C=15 inches and B = 12 inches

Substitute the value in the formula,

$15^2=A^2+12^2$

$225=A^2+144$

$A^2=225-144$

$A^2=81$

$A=\sqrt{81}$

$A=9$

Assume that A=15 inches and B = 12 inches

Substitute the value in the formula,

$C^2=15^2+12^2$

$C^2=225+144$

$C^2=369$

$C=\sqrt{369}$

$C=19.2$

Therefore, The possible length of the third side of the triangle is

$L=C-A$

$L=19.2-9$

$L=10.2$

Therefore, The difference between the two possible  lengths of the third side of the triangle is 10.2 inches.

So, Option 1 is correct.

Answer 2

Answer:

10.2 inches

Step-by-step explanation:

Ok let's assume we don't know the larger (the c value).

So this means using $a^2+b^2=c^2$ we have:

$12^2+15^2=c^2$

$144+225=c^2$

$369=c^2$

Square both sides:

$c=\sqrt{369} \aprox 19.2[/texNow assume we know the larger is 15 (this means c=15 now), then we have[tex]a^2+12^2=15^2$

$a^2+144=225$

Subtract 144 on both sides:

$a^2=225-144$

Simplify:

$a^2=81$

Square root both sides:

$a=9$

The difference between 19.2 and 9 is 19.2-9=10.2.