Question

The lengths of two sides of a right triangle are 5 inches and 8 inches. What is the difference between the two possible
lengths of the third side of the triangle? Round your answer to the ne arest tenth
3.1 inches
32 inches
10.0 inches
15.7 inches
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Answer 1

The difference between the two possible  lengths of the third side of the triangle is 3.2 inches

Solution:

Given that,

The lengths of two sides of a right triangle are 5 inches and 8 inches

Let the sides of the triangle are:

a = 5

b = 8

c = x

Case 1:

Let the third side be hypotenuse

By pythogoras theorem,

$c^2=a^2+b^2$

Therefore,

$x^2 = 5^2+8^2\\\\x^2 = 25+64\\\\x^2 = 89\\\\x = 9.433( consider\ positive\ value)$

So, first possible value of the third side is 9.433 inches

Case 2

Let 8 inches is the hypotenuse of the triangle

Therefore,

$8^2 = x^2+5^2\\\\64 = x^2+25\\\\x^2 = 64-25\\\\\x^2 = 39\\\\x = 6.245$

What is the difference between the two possible  lengths of the third side of the triangle

Difference = 9.433 - 6.245 = 3.188

$Difference \approx 3.2$

Thus the difference between the two possible  lengths of the third side of the triangle is 3.2 inches