In quadrilateral

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

Problem

In quadrilateral

ABCD

, the sides are

AB = 9\,\text{cm}

BC = 12\,\text{cm}

CD = 9\,\text{cm}

and

DA = 12\,\text{cm}

. The area of

ABCD

108\,\text{cm}^2

. (i) The diagonal

AC

divides the quadrilateral into

\triangle ABC

and

\triangle ADC

. If the two triangular areas add up to

108\,\text{cm}^2

, write an equation satisfied by the length

AC = x\,\text{cm}

. (ii) Solve the equation to determine the length of

AC

. (iii) State the perimeter of

\triangle ABC

using your result.