Question

triangle ABC is right angled at a ad is drawn perpendicular to BC if a b is equal to 5 cm and ac is equal to 12 cm find the area of triangle ABC also find the length of AD​

Answer 1

Answer:

Answer:

Area = 30 cm² and AD = 4.61 cm

Step-by-step explanation:

For better understanding of the solution see the attached figure :

\begin{gathered}\text{Area of triangle = }\frac{1}{2}\times Base\times Height\\\\\text{Area of ABC =}\frac{1}{2}\times AB\times AC\\\\Area=\frac{1}{2}\times 5\times 12\\\\\bf\implies Area = 30 \thinspace{ cm^2}\end{gathered}

Area of triangle =

2

1

×Base×Height

Area of ABC =

2

1

×AB×AC

Area=

2

1

×5×12

⟹Area=30cm

2

Now, for finding the length of AD :

Taking BC as a base and AD as a height of the triangle

\begin{gathered}\implies Area=\frac{1}{2}\times BC\times AD\\\\\implies 30=\frac{1}{2}\times 13\times AD\\\\\implies AD=\frac{30\times 2}{13}\\\\\implies AD=\frac{60}{13}\\\\\bf\implies AD=4.61\thinspace{ cm^2}\end{gathered}

⟹Area=

2

1

×BC×AD

⟹30=

2

1

×13×AD

⟹AD=

13

30×2

⟹AD=

13

60

⟹AD=4.61cm

2

Answer 2

Inright angles triangle BAC, AB=5cm and AC=12cm

Area of triangle=

2

1

×base×height=

2

1

×AB×AC

=

2

1

×5×12=30cm

2

Now, in ΔABC,

Area of triangle ABC=

2

1

×BC×AD

⇒30=

2

1

×13×AD

⇒ AD=

13

30×2

=

13

60

cm.

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