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 $12$ $12$ , $8$ $8$ , and $14$ $14$ , 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 $12$ $12$ , $8$ $8$ , and $14$ $14$ , respectively. What is the rectangle's area?

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Answer 1 · 2017-05-19T12:38:26

$\approx 125.22 square units$ $~~125.22" square units"$

Explanation:

$the area (A ) of the rectangle is$ $"the area (A ) of the rectangle is "$

$∙ A = 14 B \leftarrow length \times breadth$ $• A=14Blarr" length "xx" breadth"$

$to calculate B, use Pythagoras' theorem$ $"to calculate B, use Pythagoras' theorem"$

$that is A^{2} = B^{2} + C^{2}$ $"that is " A^2=B^2+C^2$

$\Rightarrow B = \sqrt{A^{2} - C^{2}}$ $rArrB=sqrt(A^2-C^2)$

$\Rightarrow B = \sqrt{12^{2} - 8^{2}}$ $rArrB=sqrt(12^2-8^2)$

$\Rightarrow B = \sqrt{144 - 64}$ $color(white)(rArrB)=sqrt(144-64)$

$\Rightarrow B = \sqrt{80} \leftarrow exact value$ $color(white)(rArrB)=sqrt80larr" exact value"$

$\Rightarrow area of rectangle = 14 \times \sqrt{80} \approx 125.22$ $rArr"area of rectangle "=14xxsqrt80~~125.22$

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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 $12$ $12$ , $8$ $8$ , and $14$ $14$ , 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 1212 , 88 , and 1414 , respectively. What is the rectangle's area?

1 Answer

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 $12$ $12$ , $8$ $8$ , and $14$ $14$ , respectively. What is the rectangle's area?