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 $7$ $7$ , $1$ $1$ , and $15$ $15$ , 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 $7$ $7$ , $1$ $1$ , and $15$ $15$ , respectively. What is the rectangle's area?

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Answer 1 · 2016-05-01T12:43:15

≈ 103.92 square units

Explanation:

The area of the rectangle = 15B

To calculate the value we require to find length of B.

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

For this triangle $A^{2} = B^{2} + C^{2}$ $A^2=B^2 + C^2$

$\Rightarrow B^{2} = A^{2} - C^{2} = 7^{2} - 1^{2} = 48$ $rArr B^2=A^2-C^2=7^2-1^2=48$

now $B^{2} = 48 \Rightarrow B = \sqrt{48} = \sqrt{16 \times 3} = 4 \sqrt{3}$ $B^2=48 rArr B = sqrt48=sqrt(16xx3)=4sqrt3$

hence area of rectangle $= 15 B = 15 \times 4 \sqrt{3} = 60 \sqrt{3} \approx 103.92$ $= 15B=15xx4sqrt3=60sqrt3 ≈ 103.92$

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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 $7$ $7$ , $1$ $1$ , and $15$ $15$ , 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 $7$ $7$ , $1$ $1$ , and $15$ $15$ , respectively. What is the rectangle's area?