91Ó°ÊÓ

Draw three non-congruent triangles each with perimeter20cm.

Perimeter of the rectangle is,

$\begin{array}{l}P=2(l+b)\\ Where,\\ l→length\\ b→base\end{array}$

Since the triangles are non-congruent, their dimensions are different but the perimeter must be 20cm.

So,

$\begin{array}{c}P=2(l+b)\\ 20=2(l+b)\\ l+b=10\text{ }cm\end{array}$

i.e. we must take the values of length and width in such a way that their sum is10cm .

Thus ,

$\begin{array}{l}\left(i\right)l=5cm,b=5\text{ }cm\\ \left(ii\right)l=8cm,b=2\text{ }cm\\ \left(iii\right)l=6cm,b=4\text{ }cm\end{array}$

Area of rectangles are,

$\begin{array}{c}\left(i\right)l=5cm,b=5\text{ }cm\\ A=lb\\ A=\left(5\right)\left(5\right)\\ A=25\text{ â¶Ä‰}c{m}^2\\ \left(ii\right)l=8cm,b=2\text{ }cm\\ A=lb\\ A=\left(8\right)\left(2\right)\\ A=16\text{ â¶Ä‰}c{m}^2\\ \left(iii\right)l=6cm,b=4\text{ }cm\\ A=lb\\ A=\left(6\right)\left(4\right)\\ A=24\text{ â¶Ä‰}c{m}^2\end{array}$

Therefore, the Area of triangles are$25\text{ â¶Ä‰}c{m}^2,16\text{ â¶Ä‰}c{m}^2,24\text{ â¶Ä‰}c{m}^2$

Three non-congruent triangles each with perimeter20cm .

Check all the areas and compare.

$\begin{array}{l}\left(i\right)l=5cm,b=5\text{ }cm\\ A=25\text{ â¶Ä‰}c{m}^2\\ \left(ii\right)l=8cm,b=2\text{ }cm\\ A=16\text{ â¶Ä‰}c{m}^2\\ \left(iii\right)l=6cm,b=4\text{ }cm\\ A=24\text{ â¶Ä‰}c{m}^2\end{array}$

Therefore, the rectangle having $l=5cm,b=5\text{ }cm$has the greatest area.