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Ilya [14]
4 years ago
8

The hypotenuese of an isosceles right triangle is 16 inches. The midpoints of its sides are connected to form an inscribed trian

gle, and this process is repeated, creating a third triangle inscribed in the previous one. Find the sum of the areas of these triangles if this process is continued infinitely.
Mathematics
1 answer:
ser-zykov [4K]4 years ago
3 0

Answer:

  256/3 = 85 1/3 square inches

Step-by-step explanation:

The dimensions of the first inscribed triangle are 1/2 those of the original, so its area is (1/2)² = 1/4 of the original. The area of the original is ...

  A = (1/2)bh = (1/2)(16/√2)(16/√2) = 64 . . . . square inches

The sum of an infinite series with first term 64 and common ratio 1/4 is ...

  S = a1/(1 -r) . . . . . . for first term a1 and common ratio r

  = 64/(1 -1/4) = 64(4/3) = 256/3 . . . . square inches

The sum of the areas of the triangles is 256/3 = 85 1/3 square inches.

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Answer:

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Answer this if you can
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The answer is x=y. 

You'll see if you replace all the x's with y's.



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What's the property of equality of r- 20 = 30
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Step-by-step explanation:

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3 years ago
Y=2x+1<br> y=4x-1<br> SHOW YOUR WORK PLEASE
Tanya [424]

Let's solve your system by substitution.

y=2x+1;y=4x−1

Step: Solve y=2x+1for y:

y=2x+1

Step: Substitute2x+1foryiny=4x−1:

y=4x−1

2x+1=4x−1

2x+1+−4x=4x−1+−4x(Add -4x to both sides)

−2x+1=−1

−2x+1+−1=−1+−1(Add -1 to both sides)

−2x=−2

−2x

−2

=

−2

−2

(Divide both sides by -2)

x=1

Step: Substitute1forxiny=2x+1:

y=2x+1

y=(2)(1)+1

y=3(Simplify both sides of the equation)

Answer:

x=1 and y=3

3 0
3 years ago
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