Question

ΔABC is right-angled at A. AD is perpendicular to BC, AB=5cm, BC=13 cm and AC=12 cm. Find the area of ΔABC. Also, find the length of AD.

Answer 1

Answer:

Area of Triangle = 1/2 bh

1/2 13×5 =32.5

Answer 2

Question:-

✿ΔABC is right-angled at A. AD is perpendicular to BC, AB=5cm, BC=13 cm and AC=12 cm. Find the area of ΔABC. Also, find the length of AD.

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Solution:-

$\boxed{\rm{\orange{Given \longrightarrow }}}$

• ΔABC is right-angled at "A".
• AD is perpendicular to BC.
• BC=13 cm
• AB=5cm
• AC=12 cm

$\boxed{\rm{\red{To\:Find\longrightarrow }}}$

• Area of ΔABC
• Length of AD

$\boxed{\rm{\pink{Explanation\longrightarrow }}}$

In right angles triangle BAC, AB=5cm and AC=12cm

Area of triangle,

$\sf\purple{↬}$$\dfrac{1}{2}×base×height$

$\sf\green{↬}$$\dfrac{1}{2}×AB×AC$

$\sf\orange{↬}$$\dfrac{1}{2}×5×12$=$30cm_^2$

Now, in ΔABC,

Area of triangle ABC,

$\sf\pink{↬}$$\dfrac{1}{2}×BC×AD$

$\sf\blue{↬}$$\dfrac{1}{2}×30×AD$

 $\sf\red{↬}$$AD=\dfrac{13×2}{13}=1360\:cm$

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