The area of a square is 72 square feet. What is the length of a diagonal of the square?

Question

The area of a square is 72 square feet. What is the length of a diagonal of the square?

2 Answers

Impact of this question

5011 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-07-17T20:22:44

Our keys for this problem is the pythagorean theorem and the are formula $A = l^{2}$ $A=l^2$ where $l$ $l$ is the length of the vertices.

Explanation:

So the lenght of the vertices is $l = \sqrt{A} = \sqrt{72}$ $l=sqrt(A)=sqrt(72)$ feet
If you consider the orthogonal traingle composed of two vertices and the diagonal of the square then the diagonal is the hypotenuse.
So the lenght of it is $L = \sqrt{{\sqrt{72}}^{2} + {\sqrt{72}}^{2}} = \sqrt{2 \cdot 72}$ $L=sqrt(sqrt(72)^2+sqrt(72)^2)=sqrt(2*72)$
$\sqrt{144} = 12$ $sqrt(144)=12$ feet

Answer 2 · 2017-07-20T09:43:09

See explanation.

Explanation:

First we find the side length:

$A = a^{2}$ $A=a^2$

$a = \sqrt{A} = \sqrt{72} = 6 \sqrt{2}$ $a=sqrt(A)=sqrt(72)=6sqrt(2)$

Now we can calculate the diagonal:

$d = a \sqrt{2} = 6 \sqrt{2} \sqrt{2} = 12$ $d=asqrt(2)=6sqrt(2)sqrt(2)=12$

Answer:

The diagonal is 12 feet long.

Science

Math

Humanities

... and beyond

The area of a square is 72 square feet. What is the length of a diagonal of the square?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question