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 $16$ $16$ , $4$ $4$ , and $5$ $5$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-04-01T07:33:57

$20 \sqrt{15}$ $20sqrt15$

Consider the diagram

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Use the pythagorean theorem to find $c$ $c$

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

Where $c$ $c$ is the Hypotenuse and $a, b$ $a,b$ are the other two sides

$\to 4^{2} + b^{2} = 16^{2}$ $rarr4^2+b^2=16^2$

$\to 16 + b^{2} = 256$ $rarr16+b^2=256$

$\to b^{2} = 256 - 16$ $rarrb^2=256-16$

$\to b^{2} = 240$ $rarrb^2=240$

$\Rightarrow b = \sqrt{240} = \sqrt{16 \cdot 15} = 4 \sqrt{15}$ $color(green)(rArrb=sqrt240=sqrt(16*15)=4sqrt15$

Now we need to find the area of the rectangle,Use

$A r e a = l \cdot b$ $color(blue)(Area=l*b$

Where $l and b$ $l and b$ are the sides of the rectangle

So,Area=

$\to 4 \sqrt{15} \cdot 5$ $rarr4sqrt15*5$

$\Rightarrow = 20 \sqrt{15}$ $color(green)(rArr=20sqrt15$

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 1616 , 44 , and 55 , respectively. What is the rectangle's area?