# 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 #, #7 #, and #9 #, respectively. What is the rectangle's area?

##### 1 Answer

Jul 2, 2017

#### Explanation:

#"the area of the rectangle " = color(red)(bar(ul(|color(white)(2/2)color(black)(9B)color(white)(2/2)|)))#

#"to find B use "color(blue)"Pythagoras' theorem"#

#rArrB^2=A^2-C^2#

#rArrB=sqrt(A^2-C^2)#

#color(white)(rArrB)=sqrt(14^2-7^2)=sqrt147#

#rArr" area of rectangle "=9xxsqrt147#

#color(white)(rArrarea of rectangle)~~109.12#