Question

2. Find the length of the hypotenuse in ABC, where LA = 90°,
AB = 4 cm , AC = 3 cm
​

Answer 1

Answer:

• Length of Hypotenuse of ∆ABC is 5 cm.

Step-by-step explanation:

Given :-

• ABC is a right angle triangle.
• ∠A = 90°.
• AB is of 3 cm.
• AC is of 4 cm.

To find:-

• Length of Hypotenuse means BC.

Solution:-

We will use Pythagoras theorem.

• Pythagoras theorem is the theorem which states that Square of hypotenuse is equal to the sum of squares of the other two sides of right angle triangle.

• Hypotenuse is the longest side of right angle triangle. This side is opposite to 90° angle.

• This Pythagoras theorem is written in formula as: Hypotenuse² = Base² + Perpendicular²

✽ Hypotenuse² = Base² + Perpendicular²

Hypotenuse = BC

Base = AC = 4 cm

Perpendicular = AB = 3 cm

Putting the values :

$\longrightarrow$ (BC)² = (AC)² + (AB)²

$\longrightarrow$ (BC)² = (4)² + (3)²

$\longrightarrow$ (BC)² = 16 + 9

$\longrightarrow$ (BC)² = 25

$\longrightarrow$ BC = √25

$\longrightarrow \sf \purple{\boxed{\bold{BC = 5}}}$

BC is Hypotenuse.

Therefore,

Length of Hypotenuse of ∆ABC is 5 cm.

Answer 2

Answer:

$\huge \bf \: Given$

• ABC is a right angled ∆ triangle.
• Where A = 90⁰
• AB = 4 cm
• AC = 3 cm

$\huge \bf \: To \: find$

Length of Hypotenuse ABC

$\huge \bf \: solution$

Here we will use Pythagoras theorem.

• His theorem says that the sides of a right triangle in a simple way, if the two sides are given.

Formula :-

$\huge \bf H {}^{2} = B {}^{2} + P {}^{2}$

H = Hypotenuse = BC

B = Base = AC = 3 cm

P = Perpendicular line = AB = 4 cm

$\sf {h}^{2} = {b}^{2} + {p}^{2}$

$\sf \: {h}^{2} = {AC}^{2} + {AB}^{2}$

$\sf \: {h}^{2} = {3}^{2} + {4}^{2}$

$\sf \: {h}^{2} = 9 + 16$

$\sf \: {h}^{2} = 25$

$\sf \: h \: = \sqrt{} 25$

${\small {\fbox {\green {bc \: = 5cm}}}}$

$\huge \bf \: Hypotenuse \: = 5 \: cm$