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 7/8 , 3/5 , and 4 , respectively. What is the rectangle's area?

May 15, 2016

Rectangle's area is $1.803$

Explanation:

As side A is hypotenuse and has length $\frac{7}{8}$ and C has length $\frac{3}{4}$, using Pythagoras theorem

Length of side B is $\sqrt{{\left(\frac{7}{8}\right)}^{2} - {\left(\frac{3}{4}\right)}^{2}}$

= $\sqrt{\frac{49}{64} - \frac{9}{16}} = \sqrt{\frac{49}{64} - \frac{36}{64}} = \frac{\sqrt{13}}{8}$

Now one side of rectangle is $4$ and side B is $\frac{\sqrt{13}}{8}$

Hence its area is $\frac{\sqrt{13}}{8} \times 4 = \frac{\sqrt{13}}{2} = 1.803$