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 $7$ $7$ , $2$ $2$ , and $8$ $8$ , respectively. What is the rectangle's area?

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Answer 1 · 2017-10-09T00:47:09

$A r e a_{rectangle} = 24 \sqrt{5} \approx 53.67$ $Area_("rectangle") = 24sqrt5 approx 53.67$

Draw the figure to better understand the problem:
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To find the area of the rectangle, find the side length of B first.

$B^{2} + 2^{2} = 7^{2}$ $B^2 + 2^2 = 7^2$

$B^{2} = 7^{2} - 2^{2}$ $B^2 = 7^2 - 2^2$
$B^{2} = 49 - 4 = 45$ $B^2 = 49-4 = 45$
$B = \sqrt{45}$ $B =sqrt(45)$

$B = 3 \sqrt{5}$ $B = 3sqrt5$
$B \approx 6.71$ $" "B approx 6.71$

$A r e a_{rectangle} = 8 \cdot 3 \sqrt{5}$ $Area_("rectangle") = 8*3sqrt5$

$A r e a_{rectangle} = 24 \sqrt{5} \approx 53.67$ $Area_("rectangle") = 24sqrt5 approx 53.67$

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 7 77 , 2 22 , and 8 88 , respectively. What is the rectangle's area?