Question

∆ABC is right angled at A. AD is perpendicular to
BC. If AB = 8 cm, BC = 10 cm and AC = 6 cm.
Find the area of ∆ABC. Also, find the length of AD.
plzzzzz answer fasstttttt...I need it now.....will mark u as brainlist!​

(plz do keep the answer short)::))

Answer 1

Given

★ ΔABC is a right angled triangle.

★ It is right angled at 'A'

★ AB = 8 cm

★ BC = 10 cm

★ AC = 6 cm

$\rule{300}{1}$

To Find

★ The area of ΔABC

★ Length of AD

$\rule{300}{1}$

Solution

(i) In the given question BC is the hypotenuse. Hypotenuse is the longest side of a right angled triangle.

Let's consider AB as the base and AC as the height.

Area of Triangle ⇒ $\dfrac{1}{2} \times base\times height$

Area of given triangle ⇒ $\dfrac{1}{2} \times 8 \times 6$

⇒ $\dfrac{1}{2} \times 48$

⇒ 24

∴ The area of the given triangle is 24 cm.

$\rule{300}{1}$

(ii) In the given ΔABC,  BC is perpendicular to AD.

BC ⇒ 10 cm

Area of triangle ⇒ $\dfrac{1}{2} \times base\times height$

Area of given triangle ⇒ $24 = (BC\times AD) \div 2$

Let AD be 'x'.

We'll solve this equation to find the value of AD ⇒ $(BC\times x)\div 2 = 24$

Let's solve your equation step-by-step.

$(10\times x)\div 2 = 24$

Step 1: Simplify the equation.

$(10\times x)\div 2 = 24$

$\dfrac{10x}{2} =24$

Step 2: Multiply both sides by 2.

$2 \times \dfrac{10x}{2} =2\times 24$

$10x = 48$

Step 3: Divide 10 by both sides.

$\dfrac{10x}{10}=\dfrac{48}{10}$

$\dfrac{24}{5}$

$4.8$

∴ The length of AD is 4.8 cm.

$\rule{300}{1}$

Answer 2

Answer:

We can see this is an Right Angle Triangle.

⠀

Here ∠ A = 90°

▪ Longest Side [ BC = 10 cm ] is Hypotenuse.

▪ AC = 6 cm [ Base ]

▪ AB = 8 cm [ Height ]

⠀

From another view, where ∠ D = 90°

▪ BC = 10 cm [ Base ]

▪ AD = ? [ Height ]

$\underline{\bigstar\:\textsf{According to the given Question :}}$

$:\implies\sf Area\:of\:\triangle ABC_{\angle A \:is\:90} = Area\:of\:\triangle ABC_{\angle D \:is \:90}\\\\\\:\implies\sf \dfrac{1}{2} \times Height \times Base=\dfrac{1}{2} \times Height \times Base\\\\\\:\implies\sf \dfrac{1}{2} \times AB \times AC = \dfrac{1}{2} \times AD \times BC\\\\\\:\implies\sf AB \times AC = AD \times BC\\\\\\:\implies\sf 8 \:cm \times 6 \:cm = AD \times 10 \:cm\\\\\\:\implies\sf \dfrac{8 \:cm \times 6\:cm}{10\:cm} = AD\\\\\\:\implies\sf \dfrac{48 \:cm}{10} = AD\\\\\\:\implies\underline{\boxed{\sf AD = 4.8 \:cm}}$

⠀

$\therefore\:\underline{\textsf{Hence, length of AD is \textbf{4.8 cm}}}.$