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3 years ago

Determine the missing side of the square.

Mathematics

2 answers:

Komok [63]3 years ago

5 0

Answer:

Length of the side W = 9cm

Step-by-step explanation:

A square has all sides equal. So since one side is 9cm, the rest will be 9cm as well. The side marked as 'W' is 9cm.

You can find this in another way (if the length of the sides aren't given) :-

The area is 81 $cm^{2}$

$side^{2}$ gives the area

Let's take the side as x.

So,

$x^{2}$ = Area

$x^{2}$ = 81 $cm^{2}$

x = $\sqrt{81}$

x = 9cm.

So, each side of the square would be 9cm!

Gekata [30.6K]3 years ago

4 0

Answer:

The missing side is 9cm.

How I got my answer:

1. Squares have equal sides.

2. The area is 81cm^2, so we have to divide 81 by 9.

81 : 9 = 9cm.

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Answer:

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3 years ago

Given that (x+y+z)(xy+xz+yz)=18 and that x^2(y+z)+y^2(x+z)+z^2(x+y)=6 for real numbers x, y, and z, what is the value of xyz?

worty [1.4K]

Answer:

Step-by-step explanation:

$(x+y+z)(xy+xz+yz)=18$ Equation 1

$x^2(y+z)+y^2(x+z)+z^2(x+y)=6$ Equation 2

What is the value of $xyz$ where each variable represents a real number?

Let's expand equation 1:

$(x+y+z)(xy+xz+yz)=18$

$x(xy)+x(xz)+x(yz)+y(xy)+y(xz)+y(yz)+z(xy)+z(xz)+z(yz)=18$

Simplify each term if can:

$x^2y+x^2z+xyz+y^2x+xyz+y^2z+xyz+z^2x+z^2y=18$

See if we can factor a little to get some of the left hand side of equation 2:

The first two terms have $x^2$ and if I factored $x^2$ from first two terms I would have $x^2(y+z)$ which is the first term of left hand side of equation 2.

So let's see what happens if we gather the terms together that have the same variable squared together.

$x^2y+x^2z+y^2x+y^2z+z^2y+z^2x+xyz+xyz+xyz=18$

Factor the variable squared terms out of each binomial pairing:

$x^2(y+z)+y^2(x+z)+z^2(y+x)+xyz+xyz+xyz=18$

Replace the sum of those first three terms with what it equals which is 6 from the equation 2:

$6+xyz+xyz+xyz=18$

Combine like terms:

$6+3xyz=18$

Subtract 6 on both sides:

$3xyz=12$

Divide both sides by 3:

$xyz=4$

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3 years ago