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 #, #3 #, and #5 #, respectively. What is the rectangle's area?

Answer 1

≈ 58.095 square units

The area of the rectangle = 5B (length#xx " breadth ")#
To find B use #color(blue)" Pythagoras' theorem " #
since A is the hypotenuse then # A^2 = B^2 + C^2#
hence #12^2 = B^2 + 3^2 rArr B^2 = 12^2 - 3^2 = 135#
now # B^2 = 135 rArr B =sqrt135#
thus area of rectangle # = 5sqrt135 ≈ 58.095 " square units " #
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Answer 2

To find the area of the rectangle, you need to use the fact that one of its sides is equal to one of the legs of the right triangle. Since side ( B ) is a leg of the right triangle and also a side of the rectangle, and its length is 5, the other side of the rectangle adjacent to ( B ) also has a length of 5.

Therefore, the area of the rectangle is the product of its two adjacent sides. So, the area of the rectangle is ( B \times C = 5 \times 3 = 15 ) square units.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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