Question

Radical question. calculate the length of the diagonal of a square with side length 4cm. the answer is 4sqaureroot2 but i dont know how to get it

Answer 1

use pythagoras, but only once

Answer 2

by pythagoras,
\[a^2+a^2=h^2\]\[2a^2=h^2\]\[\sqrt{2a^2}=h\]\[\sqrt{2}a=h\]

Answer 3

so whatever \(a\) is, (in your example it is 4) if \(a\) is the side of a square, then the length of the diagonal is \(a\sqrt{2}\)

Answer 4

by "only once" i mean once you do it with a variable \(a\) you do not need to redo it with 4 or 5 or 10
if the length of the side of a square is 10, then the length of the diagonal is \(10\sqrt{2}\)

Answer 5

Thanks :)

Answer 6

What about determine the length of the diagonal rectangle with dimensions 3cm x 9cm

Answer 7

again pythagoras
\[d^2=3^2+9^2\]
\[d^2=9+81=90\]
\[d=\sqrt{90}=\sqrt{9\times 10}=3\sqrt{10}\]