Question

ΔABC 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 ΔABC. Also find the length of AD.​

Answer 1

$\huge\mathfrak{\underline{Correct\: question}}$

ΔABC 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 ΔABC. Also find the length of AD.

____________________________

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

Answer

$\bold{STEP-BY-STEP-EXPLANATION}$

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

#BAL

#AnswerWithQuality

Answer 2

∆ABC is right - angled at A.

so, BC is definitely hypotenuse.

let AB is base and AC is altitude of ∆ABC.

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

now, area of triangle ∆ABC = 1/2 × base × altitude

= 1/2 × length of AB × length of AC

= 1/2 × 5cm × 12cm = 30 cm²

hence, area of ∆ABC = 30cm²

area of ∆ABC = 1/2 × length of AB × length of AC = 1/2 × length of BC × length of AD

=> 5cm × 12cm = 13cm × length of AD

=> 60/13 = length of AD

=>AD = 4.6 cm

hence, length of AD = 4.6 cm