Question

What will come in place of the question mark (?) in the equation \( 38^2 + 63^2 + (?)^2 = 6089 \) ?

• A. 26
• B. 24
• C. 28
• D. 32

Hint:

When solving equations involving squares, isolate the squared term and then take the square root of both sides. Remember to consider both positive and negative roots if the context allows.

Answer 1

The Correct Option is A

Step 1: Calculate the squares of the known numbers.
$$38^2 = 38 \times 38 = 1444$$
$$63^2 = 63 \times 63 = 3969$$
Step 2: Substitute the calculated squares into the equation.
$$1444 + 3969 + (?)^2 = 6089$$
Step 3: Add the known numbers.
$$1444 + 3969 = 5413$$
So, the equation becomes:
$$5413 + (?)^2 = 6089$$
Step 4: Isolate the term with the question mark.
Subtract 5413 from both sides of the equation:
$$(?)^2 = 6089 - 5413$$
$$(?)^2 = 676$$
Step 5: Solve for the question mark by taking the square root.
$$? = \sqrt{676}$$
$$? = 26$$