# A right triangle has sides A, B, and C. Side A is the hypotenuse and side B is also a side of a rectangle. Sides A, C, and the side of the rectangle adjacent to side B have lengths of 5 , 2 , and 4 , respectively. What is the rectangle's area?

Sep 1, 2017

$A = 4 \sqrt{21}$

#### Explanation:

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First, let's find the length of side $\text{B}$ using Pythagoras' theorem:

$R i g h t a r r o w {5}^{2} = {\text{B}}^{2} + {2}^{2}$

$R i g h t a r r o w 25 = {\text{B}}^{2} + 4$

$R i g h t a r r o w 21 = {\text{B}}^{2}$

$\therefore \text{B} = \sqrt{21}$

Both of the widths of the rectangle should be labelled $\text{B}$, as they are equal.

The area of the rectangle will be the product of its length and width:

$R i g h t a r r o w A = \text{B} \times 4$

$R i g h t a r r o w A = \left(\sqrt{21}\right) \times 4$

$\therefore A = 4 \sqrt{21}$

Therefore, the area of the rectangle is $4 \sqrt{21}$.