Question

5. The figure shows a right triangle JAK and three squares. Find the area of the square with side JK

Answer 1

The area of the square with side JK is 36

First find the side of the triangle for that we know area of square:

`X^2 = 64`
x = 8
Now, we know the other side of the triangle. In a right-angled triangle, the Pythagorean theorem relates the lengths of the sides. The theorem is given by:

`\[ c^2 = a^2 + b^2 \]`

where:

- c is the length of the hypotenuse,

- a and b are the lengths of the other two sides.

In your case, the hypotenuse (c) is given as 10, and the height (a) is given as 8. You want to find the length of the base (b).

Using the Pythagorean theorem:

`\[ 10^2 = 8^2 + b^2 \]`

Solving for \(b\):

`\[ 100 = 64 + b^2 \]`

Subtracting 64 from both sides:

`\[ b^2 = 36 \]`

Taking the square root of both sides (ignoring the negative square root in this context as length cannot be negative):

c
`v`

Therefore, b = 6 . So, the length of the base is 6 units.

To find the area (A) of a square, you can use the formula:

`\[ A = \text{side}^2 \]`

In this case, if the side of the square is 6 units, you can substitute this value into the formula:

`\[ A = 6^2 \]`

`\[ A = 36 \]`

So, the area of a square JK with a side length of 6 units is 36 square units.