Question

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 In a right angled triangle ABC,AB=8cm,BC=10cm,AC=6cm which side is the hypotenuse?

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Answer 1

The longest side of the right triangle is the hypotenuse..

Here, BC is the hypotenuse..

Also, angle A = 90°

In triangle CAB, by pythagoras theorem

${BC}^{2} = {AB}^{2} + {AC}^{2} \\ {10}^{2} = {8}^{2} + {6}^{2} \\ 100 = 64 + 36 \\ 100 = 100$

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Answer 2

Given

★ ΔABC is a right angled triangle.

★ It is right angled at 'A'

★ AB = 8 cm

★ BC = 10 cm

★ AC = 6 cm

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To Find

★ The area of ΔABC

★ Length of AD

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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 height21×base×height

Area of given triangle ⇒ \dfrac{1}{2} \times 8 \times 621×8×6

⇒ \dfrac{1}{2} \times 4821×48

⇒ 24

∴ The area of the given triangle is 24 cm.

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

BC ⇒ 10 cm

Area of triangle ⇒ \dfrac{1}{2} \times base\times height21×base×height

Area of given triangle ⇒ 24 = (BC\times AD) \div 224=(BC×AD)÷2

Let AD be 'x'.

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

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

(10\times x)\div 2 = 24(10×x)÷2=24

Step 1: Simplify the equation.

(10\times x)\div 2 = 24(10×x)÷2=24

\dfrac{10x}{2} =24210x=24

Step 2: Multiply both sides by 2.

2 {10x}{2} =2\times 242×210x=2×24

10x = 4810x=48

Step 3: Divide 10 by both sides.

\dfrac{10x}{10}={48}{10}1010x=1048

\dfrac{24}{5}524

4.84.8

∴ The length of AD is 4.8 cm.

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