Question

In a right-angled triangle, AB = 6cm, BC = 8cm, what is the length of AC ?

Answer 1

$\large\underline{\underline{ \sf \maltese{\:Question:-}}}$

In a right-angled triangle, AB = 6cm, BC = 8cm, what is the length of AC

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$\large\underline{\underline{ \sf \maltese{\:Given:-}}}$

⟹ AB = 6cm

⟹ BC = 8cm

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$\large\underline{\underline{ \sf \maltese{\:To \:Find:-}}}$

length of AC

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$\large\underline{\underline{ \sf \maltese{\:Solution:-}}}$

to find the the value of ac we use pythagoras therom

which is:$\sf\blue{\:hypotenuse ^2=side ^2 + side ^2}$

let's start:

now let's take ab and bc the side and ac as the hypotenuse.

so,

$⟹  {6}^{2} + {8}^{2} = {h}^{2} \\ ⟹ 36 + 64 = {h}^{2} \\ ⟹100 = {h}^{2} \\ ⟹ h = \sqrt{100} \\ ⟹ h = 10cm \\ \therefore \: side \: ac = \pink{\boxed{10cm}}$

✿verification:-

let's put 10 is the place of h and check weather it satisfies the rule.!

$⟹ {s}^{2} + {s}^{2} = {h}^{2} \\ ⟹ {6}^{2} + {8}^{2} = {10}^{2} \\ ⟹ 100 = 100$

hence proved side ac= 10cm

★More to know:-

pythagoras therom means that the square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides.

hope this helps.!

Answer 2

Answer:

Given :-

• In a right angled triangle, AB = 6 cm, BC = 8 cm.

To Find :-

• What is the length of AC.

Formula Used :-

By using Phythagorus Theorem we know that,

★ (AC)² = (AB)² + (BC)² ★

Solution :-

Given :

• AB = 6 cm
• BC = 8 cm

According to the question by using the formula we get,

⇒ (AC)² = (6)² + (8)²

⇒ (AC)² = 36 + 64

⇒ (AC)² = 100

⇒ AC = √100

➠ AC = 10

∴ The length of AC is 10 cm .

Let's Verify :-

↦ (AC)² = (AB)² + (BC)²

↦ (AC)² = (6)² + (8)²

Put AC = 10 we get,

↦ (10)² = 36 + 64

↦ 100 = 100

➦ LHS = RHS

Hence, Verified ✔

✪ Extra Information ✪

✦ Phythagorus Theorem :

• Phythagorus Theorem states that 'In a right angled triangle, the square of the hypotenuse side is equal to the sum of the square of other two sides'.