Question 255278
The length of a rectangle is x + 4
The width of a rectangle is x - 1
The perimeter is 46 cm 
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We can use th perimter formula as:
(i){{{P = 2L + 2W}}}
replacing x + 4 for L, x - 1 for W, and 46 for P, we get
(ii) {{{46 = 2(x+4) + 2(x-1)}}}
we solve for x as
(iii) {{{46 = 2x + 8 + 2x - 2}}}
(iv) {{{46 = 4x + 6}}}
(v) {{{40 = 4x}}}
(vi) {{{10 = x}}}
Now, the length = 14, and the width is 9.
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Using the Pythagorean theorem:
{{{a^2 + b^2 + c^2}}}
we get
{{{14^2 + 9^2 = c^2}}}
{{{196 + 81 = c^2}}}
{{{277 = c^2}}}
the diagonal, c, ~ 16.64