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 $7$ $7$ , $4$ $4$ , and $12$ $12$ , 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 $7$ $7$ , $4$ $4$ , and $12$ $12$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-05-07T14:30:33

≈ 68.93 square units

Explanation:

Here is a sketch (not to scale)

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The area of the rectangle = 12B

To calculate the area we require to know the value of B.

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

The hypotenuse is A hence $A^{2} = B^{2} + C^{2}$ $A^2=B^2+C^2$

and rearranging we get

$B^{2} = A^{2} - C^{2} = 7^{2} - 4^{2} = 33$ $B^2=A^2-C^2=7^2-4^2=33$

now $B^{2} = 33 \Rightarrow B = \sqrt{33}$ $B^2=33rArrB=sqrt33$

area of rectangle $= 12 B = 12 \times \sqrt{33} \approx 68.93 square units$ $=12B=12xxsqrt33 ≈ 68.93" square units "$

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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 $7$ $7$ , $4$ $4$ , and $12$ $12$ , respectively. What is the rectangle's area?

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Explanation:

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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 $7$ $7$ , $4$ $4$ , and $12$ $12$ , respectively. What is the rectangle's area?