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 $9$ $9$ , 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 $7$ $7$ , $2$ $2$ , and $9$ $9$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-03-25T14:10:24

≈ 60.374 square units

Explanation:

The area of the rectangle = 9B , where B has to be found.

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

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

$B^{2} = 7^{2} - 2^{2} = 49 - 4 = 45$ $B^2 = 7^2 - 2^2 = 49 - 4 = 45$

now $B^{2} = 45 \Rightarrow B = \sqrt{45}$ $B^2 = 45 rArr B = sqrt45$

and area of rectangle = 9B = $9 \times \sqrt{45} \approx 60.374$ $9xxsqrt45 ≈ 60.374$

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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 $7$ $7$ , $2$ $2$ , 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 $7$ $7$ , $2$ $2$ , and $9$ $9$ , respectively. What is the rectangle's area?