Question

Have anyone can teach me question no. 2, thank you

Answer 1

Before we concern ourselves with the said "pins", let's figure out the lengths of the squares first.

We are told that the total area of the two squares combined is 164.

we can represent one square length of one square with "x"

and represent one square length of the other square with "y"

$x^{2} + y^{2} = 164$

We are also told that the difference in length of the two squares is 2 cm.

With this we can replace the variable "y" with "x + 2" because it is 2 more than x.

$x^{2} + (x+2)x^{2} =164$$x^{2} +x^{2} +4x + 4 = 164$

$2x^{2} + 4x -160 = 0$

$x^{2} + 2x - 80 = 0$

(x - 8)(x + 10) = 0

x = 8 because there is no such thing as a negative length.

Knowing that x is 8, we can deduce that the other square's length is 10 because 8 + 2 = 10 (from the original value: x + 2).

Now, reading further, we know that we are given pins with length 2 to make the two squares. First let's visualize. We can see the pins, touching point to point, creating an outline of a square, right? This is the perimeter. First let's find the total perimeter of both the squares.

Perimeter = 4 x side length = 4 x 8 = 32

Perimeter = 4 x side length = 4 x 10 = 40

Total Perimeter = 32 + 40 = 72

Now we also know that each pin is 2 and that "z" amount of pins would be 72 in length.

2z = 72

z = 36

You would need 36 pins. Hope this helps!