Question

7. triangle ABC is right angled at A (Fig 11.25). AD is perpendicular to BC. If AB = 5 cm,
BC = 13 cm and AC = 12 cm, Find the area of triangle ABC. Also find the length of
AD.
​

Answer 1

Step-by-step explanation:

Given that:-

ΔABC is right angled at A

AD is perpendicular to BC.

AB = 5 cm, BC = 13 cm and AC = 12 cm

To find:-

The area of triangle ABC

Length of AD

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From the question it is given that,

AB = 5 cm, BC = 13 cm, AC = 12 cm

We know that,

Area of the ΔABC = ½ × base × height

= ½ × AB × AC

= ½ × 5 × 12

= 1 × 5 × 6

= 30 cm2

Now,

Area of ΔABC = ½ × base × height

30 = ½ × AD × BC

30 = ½ × AD × 13

(30 × 2)/13 = AD

AD = 60/13

AD = 4.6 cm

Therefore area of triangle ABC = 30cm^2 and length of AD = 4.6cm