Question

Find the area of triangle two sides of which are 18 cm and 10 cm and
the perimeter is 42 cm.​

Answer 1

Answer:

$\Huge{\purple {\underline {\underline {\mathbf {\color{Plum}{Answer}}}}}}$

$\large {\color{indigo}{\underline {\underline {\mathbf {\green{Given:-}}}}}}$

${\small {\mathbf {\blue{a \: = \: 18cm, \: b \: = \: 10cm, \: and \: perimeter \: = \: 42 cm}}}}$

${\small {\mathbf {\blue{Let \: c \: be \: the \: third \: side \: of \: the \: triangle. }}}}$

${\small {\mathbf {\blue{We \: know, \: \: perimeter \: = \: 2s, }}}}$

${\small {\mathbf {\red{2s = 42}}}}$

${\small {\bf {\red{s = 21}}}}$

${\small {\mathbf {\red {Again,s = \frac{(a + b + c)}{2} }}}}$

${\small {\mathbf {\pink{Put \: the \: value \: of \: s, \: we \: get }}}}$

${\small {\mathbf {\pink{21 = \frac{(18 + 10 + c)}{2} }}}}$

${\small {\mathbf {\pink {42 = 28 + c}}}}$

${\small {\mathbf {\pink{c = 14cm}}}}$

$\large {\color{blue} {\underline {\underline {\mathbf {\color{plum}{Area \: of \: triangle}}}}}}$

${\small {\bf { = }{\color{red} { \sqrt{s(s - a)(s - b)(s -c)}}}}}$

${\small {\bf{ = }{\color{red}{ \sqrt{21(21 - 18)(21 - 10)(21 - 14)}}}}}$

${\small {\bf{ = }{\color{red}{ \sqrt{21 \times 3 \times 11 \times 7}}}}}$

${\small {\bf{ = }{\color{red}{ \sqrt{4851}}}}}$

${\small {\bf{ = }{\color{red}{21 \sqrt{11}}}}}$

${\small {\bf{ = }{\color{skyblue}{Area \: = 21 \sqrt{11} {cm}^{2} }}}}$

Answer 2

Question:-

Find the area of triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm.

Solution:-

Let a,b and c be the sides of a triangle such that

a=18cm,b=10cm and a+b+c=42cm.

$\sf ∴ \: c = 42 - a - b$

$\sf↬ \: c = (42 - 18 - 10)cm = 14cm$

$\sf \: s = \frac{1}{2}(a + b + c) = \frac{1}{2} \times 42cm = 21cm$

$\sf \: s - a = (21 - 18)cm = 3cm$

$\sf \: s - b = (21 - 10)cm = 11cm$

$\sf \: s - c = (21 - 14)cm = 7cm$

$\sf ∴ Area \: of \: the \: triangle = \sqrt{s(s - a)(s - b)(s - c)}$

$\sf \: = \sqrt{21 \times 3 \times 11 \times 7 {cm}^{2} } \\ \\ \sf= \sqrt{3 \times 7 \times 3 \times 11 \times 7 {cm}^{2} } \\ \\ \sf = \sqrt{3 \times 3 \times 7 \times 7 \times 11 {cm}^{2} } \\ \\ \sf = 3 \times 7 \sqrt{11} {cm}^{2} = 21 \sqrt{11} {cm}^{2}$

Answer:-

$\mathfrak \red{21 \sqrt{11} {cm}^{2} \: is \: your \: answer.}$