[tex] \small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}[/tex]
[tex] \rule{300pt}{0.1pt}[/tex]
[tex]\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}[/tex]
By heron's formula,
[tex] \rm \text{Area of triangle =} \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where, a, b, c are sides of triangle and
[tex]\rm s=\dfrac{a+b+c}{2} [/tex]
Here, a=5 cm , b=12 cm & c=13 cm.
[tex]\[ \begin{array}{l} \\ \displaystyle\rm \therefore s=\frac{5+12+13}{2}=\frac{30}{2}=15 cm \\\\ \displaystyle\rm \therefore \text { Area }= \sqrt{15(15-5)(15-12)(15-13)} \\ \\ \displaystyle\rm\text { Area }=\sqrt{15 \times 10 \times 3 \times 2} \\ \\ \displaystyle\rm\text { Area }=30 \: cm ^{2} \end{array} \][/tex]
Now, we have, Area of triangle
[tex] \text{\( =\dfrac{1}{2} \times \) Base \( \times \) Height}[/tex]
[tex] \[ \begin{array}{l} \\ \displaystyle\rm 30=\frac{1}{2} \times 13 \times A D \\\\ \displaystyle\rm A D=\frac{30 \times 2}{13}=\frac{60}{13} \\ \\ \boxed{\color{orange} \rm A D=4.62 \: \: cm}\end{array} \][/tex]
Hence, Area of [tex]\rm \triangle A B C[/tex] is 30 cm² & AD =4.62 cm.
Copyright © 2024 EHUB.TIPS team's - All rights reserved.
Answers & Comments
Verified answer
[tex] \small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}[/tex]
[tex] \rule{300pt}{0.1pt}[/tex]
[tex]\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}[/tex]
[tex] \rule{300pt}{0.1pt}[/tex]
By heron's formula,
[tex] \rm \text{Area of triangle =} \sqrt{s(s-a)(s-b)(s-c)}[/tex]
Where, a, b, c are sides of triangle and
[tex]\rm s=\dfrac{a+b+c}{2} [/tex]
Here, a=5 cm , b=12 cm & c=13 cm.
[tex]\[ \begin{array}{l} \\ \displaystyle\rm \therefore s=\frac{5+12+13}{2}=\frac{30}{2}=15 cm \\\\ \displaystyle\rm \therefore \text { Area }= \sqrt{15(15-5)(15-12)(15-13)} \\ \\ \displaystyle\rm\text { Area }=\sqrt{15 \times 10 \times 3 \times 2} \\ \\ \displaystyle\rm\text { Area }=30 \: cm ^{2} \end{array} \][/tex]
Now, we have, Area of triangle
[tex] \text{\( =\dfrac{1}{2} \times \) Base \( \times \) Height}[/tex]
[tex] \[ \begin{array}{l} \\ \displaystyle\rm 30=\frac{1}{2} \times 13 \times A D \\\\ \displaystyle\rm A D=\frac{30 \times 2}{13}=\frac{60}{13} \\ \\ \boxed{\color{orange} \rm A D=4.62 \: \: cm}\end{array} \][/tex]
Hence, Area of [tex]\rm \triangle A B C[/tex] is 30 cm² & AD =4.62 cm.