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Question Number 202773 by ajfour last updated on 03/Jan/24

Commented by esmaeil last updated on 03/Jan/24

$o n l y t h i s ?$
Commented by mr W last updated on 03/Jan/24

$o n l y t h e d i a g o n a l o f t h e r e c t a n g l e i s$ $d e f i n e d . t h e r e i s n o u n i q u e s o l u t i o n$ $f o r t h e a r e a o f t h e r e c t a n g l e .$
Commented by mr W last updated on 03/Jan/24

Commented by mr W last updated on 03/Jan/24

$t h e n t h e q u e s t i o n i s n o t c o m p l e t e .$ $w i t h g i v e n d a t a w e c a n o n l y s a y t h a t$ $t h e l e n g t h o f t h e d i a g o n a l s i s$ $\sqrt{1^{2} + {(2 + 3)}^{2}} = \sqrt{26} .$
Commented by mr W last updated on 03/Jan/24

$t h e a r e a o f t h e r e c t a n g l e c a n b e$ $a n y v a l u e i n (0, 13] .$
Commented by ajfour last updated on 03/Jan/24

$t r u e, a g r e e d, t h a n k s!$ $w h a t i f t h e i n c l i n e d l e n g t h b e$ $a l s o g i v e n s a y L = 4 ?$
Commented by mr W last updated on 03/Jan/24

$l = (2 + 3) \tan θ + 1 = 4$ $\Rightarrow \tan θ = \frac{3}{5} \Rightarrow \cos θ = \frac{5}{\sqrt{34}}, \sin θ = \frac{3}{\sqrt{34}}$ $a = (2 + 3) \cos θ - 1 \sin θ = \frac{22}{\sqrt{34}}$ $b = (2 + 3) \sin θ + 1 \cos θ = \frac{20}{\sqrt{34}}$ $a r e a = a b = \frac{22 \times 20}{34} \approx 12.94$
Commented by ajfour last updated on 03/Jan/24

$T h a n k y o u . s o e a s y!$
Commented by mr W last updated on 03/Jan/24

$y e s s i r!$
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