# What is the diagonal of a rectangle with a 16:9 ratio (width to height respectively) and a surface area of about 320, the diagonal must be a whole number, all numbers are in inches and answer must be in inches.?

$d = 27 ' '$

#### Explanation:

a and b = sides of the retangle

$a = \left(\frac{16}{9}\right) \times b$

$a . b = 320$

$b = \frac{320}{a}$

$a = \left(\frac{16}{9}\right) \times \left(\frac{320}{a}\right)$

${a}^{2} = \frac{5120}{9}$

$a \cong 23.85$

$b \cong \frac{320}{23.85} \cong 13.4$

${d}^{2} \cong {23.85}^{2} + {13.4}^{2}$

$d \cong \sqrt{748.88} \cong 27.3 ' '$