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 $5$ $5$ , $2$ $2$ , and $4$ $4$ , respectively. What is the rectangle's area?

Question

2853 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-01T08:58:49

$A = 4 \sqrt{21}$ $A = 4 sqrt(21)$

enter image source here

This is an image I created using the information you provided.

First, let's find the length of side $B$ $"B"$ using Pythagoras' theorem:

$\Rightarrow 5^{2} = B^{2} + 2^{2}$ $Rightarrow 5^(2) = "B"^(2) + 2^(2)$

$\Rightarrow 25 = B^{2} + 4$ $Rightarrow 25 = "B"^(2) + 4$

$\Rightarrow 21 = B^{2}$ $Rightarrow 21 = "B"^(2)$

$therefore "B" = sqrt(21)$

Both of the widths of the rectangle should be labelled $"B"$ , as they are equal.

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

$Rightarrow A = "B" times 4$

$Rightarrow A = (sqrt(21)) times 4$

$therefore A = 4 sqrt(21)$

Therefore, the area of the rectangle is $4 sqrt(21)$ .

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 55 , 2 22 , and 4 44 , respectively. What is the rectangle's area?