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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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Verify that [tan(theta) + cot(theta)]^2 = sec^2(theta) + csc^2(theta)
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(tanθ + cotθ)² = sec²θ + csc²θ

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Left side equals Right side so equation is verified


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3 years ago
Find the value of X (Gotta choose at least 2)<br><br> x = 52<br> x = 2<br> x = 3<br> x = 33
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Before this problem gets  an answer, can you define "gotta." Does this work mean  isosceles?

Step-by-step explanation:

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Which expression is equivalent to (–3y – x) – (5y – 8x)? –8y – 8x –8y 7x 2y – 7x 8y 8x.
IRINA_888 [86]

The expression is equivalent to -8y + 7x.

Given

Expression; (-3y - x) - (5y - 8x)

<h3>How to find the equivalent expression?</h3>

To find the equivalent expression multiply the expression and add and simplify.

Then,

The expression is equivalent to;

 (-3y - x) - (5y - 8x)

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Hence, the expression is equivalent to -8y + 7x.

To know more about expression click the link given below.

brainly.com/question/13040575

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