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3 years ago

A square has side length 10 yd. What is the length of a diagonal of the square?

Mathematics

1 answer:

Vsevolod [243]3 years ago

3 0

Answer:

10√2

Step-by-step explanation:

Lets cut the square into a triangle, making a line from one corner to another, then let's see what we have.

We shoupd have a triangle where we don't know the hypotenuse, which we can find using the formula: a^2 + b^2 = c^2

so:

10^2 + 10^2 = c^2

100 + 100 = c^2

c^2 = 200

now let's square root what we got

√200

there are 2 10's in 200, which will turn the equation to:

10√2

this can't be simplified further, so our answer is 10√2

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2 years ago

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Work out the size of one of the exterior angles

hodyreva [135]

Given Information :-

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A polygon with 10 sides ( Decagon )

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To Find :-

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The value of one of the exterior angles

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Formula Used :-

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$\qquad \diamond \: \underline{ \boxed{ \pink{ \sf Exterior ~angle = \dfrac {360^\circ}{no. ~of~sides}}}} \: \star$

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Solution :-

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Putting the given values, we get,

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$\sf \dashrightarrow Exterior ~angle = \dfrac{360 ^\circ}{10} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \frac{36 \cancel{0}^\circ}{ \cancel{10}} \: \: \\ \\ \\ \sf \dashrightarrow Exterior ~angle = \underline{ \boxed{ \frak{ \red{36^\circ}}}} \: \star \\ \\$

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$\underline{ \rule{227pt}{2pt}} \\ \\$

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2 years ago

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the sum of two numbers is 18. twice the first number increased by three times the second number equals 40. find the numbers

ryzh [129]

Answer:

4 and 14

Step-by-step explanation:

:the sum of two numbers is 18" can be written as

x + y = 18 let x represent the first number, and y the second

"twice the first number increased by three times the second number equals 40" can be written as

2x + 3y = 40

Now solve this system. Using elimination will probably be the easier method...

1. x + y = 18

2. 2x + 3y = 40

Multiply equation 1 by -2 so the x variable will be the opposite of the x variable on equation 2.

1. -2x - 2y = -36

2. 2x + 3y = 40

Now add the equations together, cancelling out 'x'

y = 4 ( 2x + (-2x) = 0, so 'x' is gone, 3y + (-2y) = y, 40 + (-36) = 4)

Since y = 4, plug that into either equation 1 or 2 and solve for x

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x = 14 (subtract 4 on both sides to isolate 'x')

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