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Sliva [168]
3 years ago
13

What is the ratio of the area of the inner square to the area of the outer square?

Mathematics
2 answers:
Anastasy [175]3 years ago
4 0

Answer:

\frac{(a-b)^2+b^2}{a^2}

Step-by-step explanation:

Since, By the given diagram,

The side of the inner square = Distance between the points (0,b) and (a-b,0)

=\sqrt{(a-b-0)^2+(0-b)^2}

=\sqrt{(a-b)^2+b^2}

Thus the area of the inner square = (side)²

=(\sqrt{(a-b)^2+b^2})^2

=(a-b)^2+b^2\text{ square cm}

Now, the side of the outer square = Distance between the points (0,0) and (a,0),

=\sqrt{(a-0)^2+0^2}

=\sqrt{a^2}=a

Thus, the area of the outer square = (side)²

=a^2\text{ square cm}

Hence, the ratio of the area of the inner square to the area of the outer square

=\frac{(a-b)^2+b^2}{a^2}

8090 [49]3 years ago
4 0

Answer:

I got this fraction:

frac{(a-b)^2+b^2}{a^2}

(I got the answer correct)

Hope this is helpful :)

Step-by-step explanation:

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2 years ago
Solve the system by substitution.<br> x – 4y = -8<br> 5у – 1 = x<br> Submit Answer
Vikki [24]

Answer:

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Step-by-step explanation:

x - 4y = -8

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→ Substitute 5y - 1 into x - 4y = -8

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→ Simplify

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7 0
3 years ago
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aliya0001 [1]

For this case we have:

By properties of the radicals \sqrt {a} = a ^{\frac {1} {2}}

So:

(\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2.

Now, for power properties we have:

(b ^ {\frac {c} {d}}) ^ e = b ^ {\frac {c * e} {d}}

Thus, (7 ^ {\frac {1} {2}}) ^ 2 = 7 ^ {\frac {2} {2}} = 7

So:

7 ^ {\frac {1} {2}} = \sqrt {7}in its radical form

Answer:

(\sqrt {7}) ^ 2 = (7 ^ {\frac {1} {2}}) ^ 2= 7 ^ {\frac {2} {2}} = 7 in its simplest form.

7 ^ {\frac {1} {2}} = \sqrt {7}in its radical form


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