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 #, #4 #, and #1 #, respectively. What is the rectangle's area?

Answer 1

The rectangle's area is #sqrt(33)# or #5.74#

Above is a drawing of the situation in question.

Since we have two sides of a right triangle, we can use the Pythagorean theorem to calculate the length of side B.

#a^2+b^2=c^2#

Be sure to note that a and b here refer to the smaller sides of the triangle and the c refers to hypotenuse, which is different from the letters in our diagram!

#4^2+b^2=7^2#

#16+b^2=49#

#b^2=33#

#b=sqrt(33)#

Now, to calculate the area of the rectangle, we must multiple its length by its width. Side B is its length and we already know its width is 1, and since any number multiple by 1 is just itself, the area of the rectangle is #sqrt(33)#, or #5.74#

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Answer 2

Carson Arnold

The rectangle's area is 4 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.