4.
The formula for the diagonal of a rectangle is:
[tex]\sf D=\sqrt{l^2+w^2}[/tex]
Plug in what we know:
[tex]\sf D=\sqrt{4^2+3^2}[/tex]
Simplify the exponents:
[tex]\sf D=\sqrt{16+9}[/tex]
Add:
[tex]\sf D=\sqrt{25}[/tex]
Take the square root:
[tex]\sf D=\boxed{\sf 5~in}[/tex]
For the second one, we know that the area of a square is:
[tex]\sf A=s^2[/tex]
Plug in what we know:
[tex]\sf 25=s^2[/tex]
Take the square root of both sides:
[tex]\sf s=5[/tex]
So we know that the length and width are both 5 meters long, let's plug this into the formula for the diagonal:
[tex]\sf D=\sqrt{5^2+5^2}[/tex]
Simplify the exponents:
[tex]\sf D=\sqrt{25+25}[/tex]
Add:
[tex]\sf D=\sqrt{50}[/tex]
Take the square root:
[tex]\sf D\approx\boxed{\sf 7.07~m}[/tex]
