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 $3$ $3$ , $1$ $1$ , and $9$ $9$ , respectively. What is the rectangle's area?

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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 $3$ $3$ , $1$ $1$ , and $9$ $9$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-06-01T10:49:04

$18 \sqrt{2}$ $18sqrt(2)$

Explanation:

Given $A = 3$ $A=3$ and $C = 1$ $C=1$
by the Pythagorean Theorem
$XXX B = \sqrt{3^{2} - 1^{1}} = 2 \sqrt{2}$ $color(white)("XXX")B=sqrt(3^2-1^1)=2sqrt(2)$

Since the rectangle has sides of length $B$ $B$ and $9$ $9$
the rectangle's area is
$XXX 2 \sqrt{2} \times 9 = 18 \sqrt{2}$ $color(white)("XXX")2sqrt(2)xx9=18sqrt(2)$

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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 $3$ $3$ , $1$ $1$ , and $9$ $9$ , respectively. What is the rectangle's area?

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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 33 , 11 , and 99 , respectively. What is the rectangle's area?

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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 $3$ $3$ , $1$ $1$ , and $9$ $9$ , respectively. What is the rectangle's area?