Question

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Find the missing side of the triangle.

Answer 1

x = 45

Explanation:

Forming the equation,

→ (x)² = (36)² + (27)²

Now the value of x will be,

→ (x)² = (36)² + (27)²

→ x² = 1296 + 729

→ x² = 2025

→ x = √2025

→ [ x = 45 ]

Hence, the value of x is 45.

Answer 2

Missing side length = 45

Explanation:

In this problem, we're trying to find the longest side, or hypotenuse, of the triangle. Luckily, there's a formula to find this!

The Pythagorean Theorem

The Pythagorean Theorem is a formula that allows us to find any of the three sides of a right triangle using the lengths of the other two sides.

The formula is, a² + b² = c², where a and b are the side lengths of the two sides that make the right angle and c is the length of the side across from the right angle, the hypotenuse.

To use the formula, we just have to plug in the lengths of the two sides we know and then solve for the third variable. When we're looking for the hypotenuse length, we'll plug in the values for a and b, then solve for c. The a and b values are completely interchangeable, so it won't matter which side length you plugin for which. You just have to make sure that c is going to be the hypotenuse length.

Solving the Equation

Let's go ahead and plug in our known values for the equation. We're given the two side lengths 27 and 36, which will be our a and b values. Remember, they're interchangeable!

27² + 36² = c² Next, we can square the a and b numbers.

729 + 1296 = c² Now add them together.

2025 = c² And finally, square root both sides of the equation.

`√(2025)= √(c^2)`

45 = c

So, the length of the hypotenuse for this triangle is 45. Now, you can use this formula to solve for any of the three sides of a right triangle when given the other two side lengths.