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 $8$ $8$ , $7$ $7$ , and $7$ $7$ , 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 $8$ $8$ , $7$ $7$ , and $7$ $7$ , respectively. What is the rectangle's area?

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Answer 1 · 2017-06-09T19:19:26

$\approx 27.11 square units$ $~~27.11" square units"$

Explanation:

$the area of the rectangle = length \times breadth$ $"the area of the rectangle = length " xx" breadth"$

$\Rightarrow area = 7 B \leftarrow require to find B$ $rArr"area " =7color(red)(B)larr" require to find "color(red)(B)$

$to calculate B use Pythagoras' theorem$ $"to calculate "color(red)(B)" use "color(blue)"Pythagoras' theorem"$

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

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

$\Rightarrow B = \sqrt{8^{2} - 7^{2}}$ $color(white)(rArrB)=sqrt(8^2-7^2)$

$\Rightarrow B = \sqrt{15}$ $color(white)(rArrB)=sqrt15$

$\Rightarrow area = 7 B = 7 \sqrt{15} \approx 27.11 square units$ $rArr"area "=7B=7sqrt15~~27.11" square units"$

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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 $8$ $8$ , $7$ $7$ , and $7$ $7$ , 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 88 , 77 , and 77 , 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 $8$ $8$ , $7$ $7$ , and $7$ $7$ , respectively. What is the rectangle's area?