Question

In a right triangle ABC cb =90 degree if AB = 5cm , bc = 12 cm then find AC

Answer 1

${\underline{\underline{\red{\sf{Given:}}}}}$

• There is a right angled ∆ABC.
• The measure of AB = 5cm.
• The measure of BC =12cm.

${\underline{\underline{\red{\sf{To\:Find:}}}}}$

• Measure of side AC .

${\underline{\underline{\red{\sf{Concept\;Used:}}}}}$

• We will make use of Pythagoras Theorm.

${\underline{\underline{\red{\sf{Answer:}}}}}$

We are given a right angled triangle .

So , 'Pythagoras Theorem' is applicable here .

Now Pythagoras Theorem is stated as :

• The square of hypotenuse is equal to sum of square of other two sides.

$\large{\boxed{\red{\sf{\hookrightarrow AC^{2}=AB^{2}+BC^{2}}}}}$

(For figure refer to attachment:)

$\sf{\implies AC^{2}=(5cm)^{2}+(12cm)^{2}}$

$\sf{\implies AC^{2}=25cm^{2}+144cm^{2}}$

$\sf{\implies AC^{2}=169cm^{2}}$

$\sf{\implies AC=\sqrt{169cm^{2}}}$

${\underline{\boxed{\purple{\sf{\longmapsto AC=13cm}}}}}$

Therefore length of side AC is 13cm.

Note:

1. Here 5 cm ,12cm & 13cm are Pythagorean Triplet.

Answer 2

Answer:

{\underline{\underline{\red{\sf{Given:}}}}}

Given:

There is a right angled ∆ABC.

The measure of AB = 5cm.

The measure of BC =12cm.

{\underline{\underline{\red{\sf{To\:Find:}}}}}

ToFind:

Measure of side AC .

{\underline{\underline{\red{\sf{Concept\;Used:}}}}}

ConceptUsed:

We will make use of Pythagoras Theorm.

{\underline{\underline{\red{\sf{Answer:}}}}}

Answer:

We are given a right angled triangle .

So , 'Pythagoras Theorem' is applicable here .

Now Pythagoras Theorem is stated as :

The square of hypotenuse is equal to sum of square of other two sides.

\large{\boxed{\red{\sf{\hookrightarrow AC^{2}=AB^{2}+BC^{2}}}}}

↪AC

2

=AB

2

+BC

2

(For figure refer to attachment:)

\sf{\implies AC^{2}=(5cm)^{2}+(12cm)^{2}}⟹AC

2

=(5cm)

2

+(12cm)

2

\sf{\implies AC^{2}=25cm^{2}+144cm^{2}}⟹AC

2

=25cm

2

+144cm

2

\sf{\implies AC^{2}=169cm^{2}}⟹AC

2

=169cm

2

\sf{\implies AC=\sqrt{169cm^{2}}}⟹AC=

169cm

2

{\underline{\boxed{\purple{\sf{\longmapsto AC=13cm}}}}}

⟼AC=13cm

Therefore length of side AC is 13cm.

Note:

Here 5 cm ,12cm & 13cm are Pythagorean Triplet.