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 $3$ , $2$ , and $5$ , respectively. What is the rectangle's area?

Question

1653 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-12T09:08:02

$Area=5sqrt5$

Consider the diagram

enter image source here

We need to find the length $B$

$color(blue)(a^2+b^2=c^2$

Where

$color(red)(c=Hypoten$ $color(red)(use$

$color(red)(a andb=other$ $color(red)(two$ $color(red)(sides$

But, In this case $A$ is the $Hypoten$ $use$

$:.2^2+B^2=3^2$

$rarr4+B^2=9$

$rarrB^2=9-4$

$rarrB^2=5$

$rArrB=sqrt5$

We find that $B$ is one of the side of the rectangle

$Area$ $of$ $recta$ $ngl$ $e=l*b$ $units$

$color(green)( :.Area=sqrt5*5=5sqrt5$

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 3 3 , 2 2 , and 5 5 , respectively. What is the rectangle's area?