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 $10$ $10$ , $8$ $8$ , and $4$ $4$ , 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 $10$ $10$ , $8$ $8$ , and $4$ $4$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-04-08T19:26:15

24 square units

Explanation:

The area of the rectangle = $4B$ $color(blue)" 4B"$

To calculate the value of the area , require to find B.

Since the triangle is right with hypotenuse A , we can use $Pythagoras' theorem to find B$ $color(red)" Pythagoras' theorem " " to find B"$

$A^{2} = B^{2} + C^{2} \Rightarrow B^{2} = A^{2} - C^{2}$ $A^2 = B^2 +C^2 rArr B^2 = A^2 - C^2$

$\Rightarrow B^{2} = 10^{2} - 8^{2} = 100 - 64 = 36$ $rArr B^2 = 10^2 - 8^2 = 100 - 64 = 36$

now $B^{2} = 36 \Rightarrow B = \sqrt{36} = 6$ $B^2 = 36 rArr B = sqrt36 = 6$

and area of rectangle = 4B $= 4 \times 6 = 24 square units$ $= 4xx6 = 24" square units "$

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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 $10$ $10$ , $8$ $8$ , and $4$ $4$ , 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 $10$ $10$ , $8$ $8$ , and $4$ $4$ , respectively. What is the rectangle's area?