Mathematics: Consider the rectangle: 4V20 + 2V24 3V8 Select all expressions that are equivalent to the perimeter of the rectangle.HELP ASAP PLZ.

Its alternate interiorHope this helped :)...

Consider the rectangle: 4V20 + 2V24 3V8 Select all

sashllely6112

20.03.2022

The perimeter of a rectangle is the sum of visible lengths of the rectangle. The equivalent expressions are:

$P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)$

$P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})$

$P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}$

Given that:

$L = 4\sqrt{20} + 2\sqrt{24}$ --- Length

$W = 3\sqrt 8$ --- Width

The perimeter (P) of the rectangle is:

$P = 2 \times (L + W)$

So, we have:

$P = 2 \times (4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)$

$P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)$

Rewrite as:

$P = 2( 3\sqrt 8+4\sqrt{20} + 2\sqrt{24})$

Expand

$P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})$

Further expand

$P = 6\sqrt 8 +8\sqrt{20} + 2\sqrt{24}$

$P = 6\sqrt{4\times 2} +8\sqrt{4\times 5} + 2\sqrt{4\times 6}$

Evaluate square roots

$P = 6 \times 2\sqrt{2} +8\times 2\sqrt{5} + 2\times 2\sqrt{6}$

$P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}$

Hence, the equivalent expressions are:

$P = 2(4\sqrt{20} + 2\sqrt{24} + 3\sqrt 8)$

$P = 2(3\sqrt 8) +2(4\sqrt{20} + 2\sqrt{24})$

$P = 12\sqrt{2} + 16\sqrt{5} + 4\sqrt{6}$