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 $11$ , $6$ , and $13$ , respectively. What is the rectangle's area?

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Answer 1 · 2018-02-09T03:11:22

Area of rectangle $approx 120$

Given:
In triangle $ABC$
$A$ is hypotenuse = 11
$C$ = 6
So, B is the other side of the right angled triangle.
Let us find B using Pythagoras theorem:

$=> A^2 = B^2 + C^2$

$=> B^2 = A^2- C^2$

$=> B^2 =11^2 - 6^2$

$=> B^2 = 121-36 = 85$

$=> B = sqrt 85$

$=> B approx 9.22$

Also given the length of side of rectangle adjacent to B = 13

$=>$ sides of rectangle are B =9.22 and adjacent side =13.
So, area of rectangle will be:

$therefore Area = 9.22 xx 13 = 119.86 approx 120$

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 11 11 , 6 6 , and 13 13 , respectively. What is the rectangle's area?