Atriangle has side legnths of 11cm and 9cm. which could be the value of the third side

2√10 ; √202

Step-by-step explanation:

There can be two answers for you to get:

1) Assuming that 11 is the hypotenuse (the longest side), and solving for the shorter side (x).

2) Assuming that the third side (x) is the hypotenuse, and that all the other lengths given are shorter.

In scenario 1:

use the formula: c² - b² = a², in which c = hypotenuse, and a and b = shorter sides.

Plug in the numbers:

hypotenuse = c = 11

side = b = 9

side = a = what we are solving for

(11)² - (9)² = a²

Simplify.

(11)² = 11 * 11 = 121

(9)² = 9 * 9  = 81

Subtract to get the side (a) in a²:

121 - 81 = 40

a² = 40

Root both sides to isolate a (and get the answer for a).

√(a²) = √(40)

a = √40 = √(2 * 2 * 2 * 5) = 2√10

2√10 is one of your answer choices.

In scenario 2:

use the formula a² + b² = c², in which c = hypotenuse, and a and b = shorter sides.

Plug in the numbers:

hypotenuse = c = what we are solving for

side = a = 11

side = b  = 9

(11)² + (9)² = c²

Simplify.

11 * 11 = 121

9 * 9 = 81

121 + 81 = c²

c² = 202

Isolate the c. Root both sides of the equation.

√(c²) = √(202)

c = √202

√202 cm. is your answer, for it cannot be simplified any further.

Decimal answer rounded is 14.21 cm.

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