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 $14$ , $4$ , and $3$ , respectively. What is the rectangle's area?

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Answer 1 · 2017-12-24T14:47:28

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The image above is the shapes we are dealing with from the question.

We can use the Pythagorean Theorem to find the length of $B$ .

The Pythagorean Theorem states:

$B^2 + C^2 = A^2$ where $A$ is the hypotenuse of a right triangle.

Substituting the values from the problem and solving $B$ gives:

$B^2 + 4^2 = 14^2$

$B^2 + 16 = 196$

$B^2 + 16 - color(red)(16) = 196 - color(red)(16)$

$B^2 + 0 = 180$

$B^2 = 180$

$sqrt(B^2) = sqrt(180)$

$B = sqrt(36 * 5)$

$B = sqrt(36)sqrt(5)$

$B = 6sqrt(5)$

The formula for the area of a rectangle is:

$A = l xx w$

Substituting the value from the problem and the value we calculated and calculating $A$ gives:

$A = 6sqrt(5) xx 3$

$A = 18sqrt(5)$

Or

$A = 40.25$ rounded to the nearest hundredth

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 14 14 , 4 4 , and 3 3 , respectively. What is the rectangle's area?