A triangle has fixed perimeter

MATHEMATICS · Subjective · CBSE · Mathematics · Heron's Formula · Heron's Formula

Problem

30\,\text{cm}

. Two of its sides are equal, each measuring

x\,\text{cm}

, and the third side measures

(30-2x)\,\text{cm}

. (i) Write an expression for the semi-perimeter in terms of

x

. (ii) Hence obtain an expression for the area

\Delta

of the triangle in terms of

x

. (iii) The triangle can exist only if

30-2x>0

and

x+x>30-2x

. State the integer values of

x

that satisfy these conditions. (iv) Using the values of

x

found in (iii), determine the value of

x

for which the area of the triangle is maximum. Also find this maximum area correct to two decimal places.