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 $12$ $12$ , $4$ $4$ , and $9$ $9$ , respectively. What is the rectangle's area?

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Answer 1 · 2018-02-18T03:01:39

Area of rectangle, $A_{r} = l \cdot b = 9 \cdot 11.3137 \approx 101.8234$ $A_r = l * b = 9 * 11.3137 ~~ color (green)(101.8234)$

Given : $a = 12, c = 4$ $a = 12, c = 4$ , length of rectangle $l = 9$ $l = 9$

To find $b$ $b$ , width of rectangle and area of rectangle.

Applying Pythagoras theorem,

$b = \sqrt{a^{2} - c^{2}} = \sqrt{12^{2} - 4^{2}} = 11.3137$ $b = sqrt (a^2 - c^2) = sqrt(12^2 - 4^2) =color(blue)( 11.3137$

b is also the width of the triangle.

$.$ $.$ Area of rectangle, $A_{r} = l \cdot b = 9 \cdot 11.3137 \approx 101.8234$ $A_r = l * b = 9 * 11.3137 ~~ color (green)(101.8234)$

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 1212 , 44 , and 99 , respectively. What is the rectangle's area?