Question

I'll Mark you as a brainliest pls answer this question

Answer 1

$\small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}$

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By heron's formula,

$\rm \text{Area of triangle =} \sqrt{s(s-a)(s-b)(s-c)}$

Where, a, b, c are sides of triangle and

$\rm s=\dfrac{a+b+c}{2}$

Here, a=5 cm , b=12 cm & c=13 cm.

$\[ \begin{array}{l} \\ \displaystyle\rm \therefore s=\frac{5+12+13}{2}=\frac{30}{2}=15 cm \\\\ \displaystyle\rm \therefore \text { Area }= \sqrt{15(15-5)(15-12)(15-13)} \\ \\ \displaystyle\rm\text { Area }=\sqrt{15 \times 10 \times 3 \times 2} \\ \\ \displaystyle\rm\text { Area }=30 \: cm ^{2} \end{array} \]$

Now, we have, Area of triangle

$\text{\( =\dfrac{1}{2} \times \) Base \( \times \) Height}$

$\[ \begin{array}{l} \\ \displaystyle\rm 30=\frac{1}{2} \times 13 \times A D \\\\ \displaystyle\rm A D=\frac{30 \times 2}{13}=\frac{60}{13} \\ \\ \boxed{\color{orange} \rm A D=4.62 \: \: cm}\end{array} \]$

Hence, Area of $\rm \triangle A B C$ is 30 cm² & AD =4.62 cm.