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 $5$ $5$ , $4$ $4$ , and $11$ $11$ , respectively. What is the rectangle's area?

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Answer 1 · 2017-03-06T06:02:12

The area of the rectangle is $33$ $33$ .

From the data given we can draw the following shape:

Self-drawn
Since the triangle is right angled, we can determine the length of B using the Pythagorean theorem.

$B^{2} + C^{2} = A^{2}$ $B^2+C^2=A^2$

$B^{2} + 4^{2} = 5^{2}$ $B^2+4^2=5^2$

$B^{2} + 16 = 25$ $B^2+16=25$

Subtract $16$ $16$ from each side.

$B^{2} = 25 - 16$ $B^2=25-16$

$B^{2} = 9$ $B^2=9$

Determine the square root.

$B = 3$ $B=3$

Since we know that $B = 3$ $B=3$ and that the side adjacent to $B$ $B$ is $11$ $11$ , the area of the rectangle can be calculated using the formula:

$A = l \times h$ $A=lxxh$

where $l =$ $l=$ length ( $11$ $11$ ) and $h =$ $h=$ height (in this case: $B = 11$ $B=11$ )

$A = 3 \times 11$ $A=3xx11$

$A = 33$ $A=33$

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 , 4 44 , and 11 1111 , respectively. What is the rectangle's area?