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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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