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In the figure, a square is inside another bigger square.

If a = 4 units and b = 3 units, the length of the diagonal of the outside square rounded to the nearest tenth is _____
units and the length of the diagonal of the inside square rounded to the nearest tenth is _____ units.

In the figure a square is inside another bigger square If a 4 units and b 3 units the length of the diagonal of the outside square rounded to the nearest tenth class=

Respuesta :

calculista

Answer:

Part 1) The length of the diagonal of the outside square is 9.9 units

Part 2) The length of the diagonal of the inside square is 7.1 units

Step-by-step explanation:

step 1

Find the length of the outside square

Let

x -----> the length of the outside square

c ----> the length of the inside square

we know that

[tex]x=a+b=4+3=7\ units[/tex]

step 2

Find the length of the inside square

Applying the Pythagoras Theorem

[tex]c^{2}= a^{2}+b^{2}[/tex]

substitute

[tex]c^{2}= 4^{2}+3^{2}[/tex]

[tex]c^{2}=25[/tex]

[tex]c=5\ units[/tex]

step 3

Find the length of the diagonal of the outside square

To find the diagonal Apply the Pythagoras Theorem

Let

D -----> the length of the diagonal of the outside square

[tex]D^{2}= x^{2}+x^{2}[/tex]

[tex]D^{2}= 7^{2}+7^{2}[/tex]

[tex]D^{2}=98[/tex]

[tex]D=9.9\ units[/tex]

step 4

Find the length of the diagonal of the inside square

To find the diagonal Apply the Pythagoras Theorem

Let

d -----> the length of the diagonal of the inside square

[tex]d^{2}= c^{2}+c^{2}[/tex]

[tex]d^{2}= 5^{2}+5^{2}[/tex]

[tex]d^{2}=50[/tex]

[tex]d=7.1\ units[/tex]

Answer:

its 7 and 10 in the blanks im pretty sure.

Step-by-step explanation:

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