# How do you find the perimeter of a rectangle, in simplest radical form, in which the base is sqrt98 and the height is 5sqrt2?

Oct 29, 2016

34

#### Explanation:

$\sqrt{98} = 9.9$
$5 \cdot \sqrt{2} = 7.1$
Since two sides of the rectangle are 9.9 in length,
$2 \cdot 9.9 = 19.8$
Since the other two sides of the rectangle are 7.1 in length,
$2 \cdot 7.1 = 14.2$
Therefore, the total length of the perimeter of the rectangle is,
$19.8 + 14.2 = 34.0$

Oct 29, 2016

The given rectangle has

$b a s e = \sqrt{98} = \sqrt{{7}^{2} \cdot 2} = 7 \sqrt{2}$

and

$h e i g h t = 5 \sqrt{2}$

So

$P e r i m e t e r = 2 \left(b a s e + h e i g h t\right) = 2 \left(7 \sqrt{2} + 5 \sqrt{2}\right) = 2 \cdot 12 \sqrt{2} = 24 \sqrt{2}$