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Iteru [2.4K]
2 years ago
8

Context/Question: Rachel bought a framed piece of artwork as a souvenir from her trip to Disney World. The diagonal of the frame

is 20 inches. If the length of the frame is 4 inches greater than it’s width, find the dimensions of the frame.
Answer: The length is __ in. and the width is __ in.
Mathematics
1 answer:
Stolb23 [73]2 years ago
7 0

The diagonal of a rectangular figure is an illustration of Pythagoras theorem

The length is 16 in, and the width is 12 in

The given parameters are:

\mathbf{Diagonal = 20}

\mathbf{Length = 4 + Width}

The diagonal is calculated using, the following Pythagoras theorem

\mathbf{Diagonal^2 = Length^2 + Width^2}

Represent length with L and width with W

So, we have:

\mathbf{20^2 = L^2 + W^2}

\mathbf{400 = L^2 + W^2}

This gives

\mathbf{400 = (4 + W)^2 + W^2}

Expand

\mathbf{400 = 16 + 8W + W^2 + W^2}

\mathbf{400 = 16 + 8W + 2W^2}

Divide through by 2

\mathbf{200 = 8 + 4W +W^2}

Rewrite as:

\mathbf{W^2 + 4W +8 -200 = 0}

\mathbf{W^2 + 4W - 192 = 0}

Using a calculator, we have:

\mathbf{W = \{-16,12\}}

The width cannot be negative.

So, we have:

\mathbf{W =12}

Recall that:

\mathbf{Length = 4 + Width}

This gives

\mathbf{L= 4 + 12}

\mathbf{L= 16}

Hence, the length is 16 in, and the width is 12 in

Read more about diagonals at:

brainly.com/question/18983839

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Find the length of side AB in the right triangle shown.
Bogdan [553]
Side AB is 72 cm long.



Explanation:

To find the length of side AB you have to use this formula:

{a}^{2}  +  {b}^{2}  =  {c}^{2}

*Remember there are two legs (a and b) and a hypotenuse (c) on a triangle. The longest side will be the hypotenuse and the other two will be the legs. For this triangle the hypotenuse is side BC while the legs are sides CA and side AB.

Plug in the numbers into the equation.


{65}^{2}  +  {b}^{2}  =  {97}^{2}
For this triangle, you were given the hypotenuse (c) and one leg (a). To find the last length solve the equation and balance it so only b is left, like this:

4225 +  {b}^{2}  = 9409

9409 - 4225 = 5184

Soo...

{b}^{2}  = 5184

Then to get the side length, square root 5184.

\sqrt{5184}  = 72

So the length of the last side is 72 cm.
5 0
3 years ago
X - y = 2<br> 4x – 3y = 11
swat32

Answer:

<u><em>For x - y = 2</em></u>

You need to find x or y in one of the equations and then substitute that into the other.

So we have;

x-y=2

4x-3y=11

We will take the first equation and find x;

x-y=2

add y to both sides;

x-y+y=2+y

x=2+y

Now we take that answer and substitute it forx in the other equation;

 

4(2+y)-3y=11

8+4y-3y=11

8+y=11

y=3

Now we have what y equals, so we use it in the first equation to find x;

x-3=2

x=5

So we have;

x=5; y=3

Hope you understand!

=)

<u><em>And for 4x – 3y = 11</em></u>

Multiply the first equation by 2 and the second by 3 so that there are the same number of y's in each:

8x - 6y = 22    ...(3)

30x + 6y = -3  ...(4)

 Now add (3) and (4) term by term:

38x + 0 = 19

or

38x = 19

or x = 1/2

Put this back into equation (1)

4*(1/2) - 3y = 11

or

2 - 3y = 11

Subtract 2 from both sides:

-3y = 9

 Divide both sides by -3

y = -3

6 0
3 years ago
Read 2 more answers
Evaluate f(x)=-4x-5 for x = -1
Lubov Fominskaja [6]
F(x)=-4(-1)-5 
f(x)=4-5
f(x)= -1
-1 is your answer 
5 0
3 years ago
6 x 20 = 6 x ___ tens= ___tens = ____
Gekata [30.6K]
6x20=6x2 tens=12tens=120
8 0
3 years ago
Simplify: -2 1/3 - (-10 1/6) 1) -12 1/2 2) 12 1/2 3) 7 5/6 4) -7 5/6
marshall27 [118]

Answer:

- 5 16/22

Step-by-step explanation:

idk

7 0
3 years ago
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