Question

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.

Answer 1

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:

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