Question

What is the area
of a right triangle whose
hypotenuse is 10m and base = 6m?​

Answer 1

Answer:

‎ ‎$\underline{\large\sf{Answer♡}}$ ‎ ‎ ‎ ‎ ‎

Step-by-step explanation:

$\sf \huge \purple { Area=24m²}$

Answer 2

$\begin{gathered}\begin{gathered}\bf \:Given\: -\begin{cases} &\sf{hypotenuse \: = \: 10 \: m} \\ &\sf{base \: = \: 6 \: m} \end{cases}\end{gathered}\end{gathered}$

$\begin{gathered}\begin{gathered}\bf \:To\: find\:-\begin{cases} &\sf{area \: of \: right \: triangle}  \end{cases}\end{gathered}\end{gathered}$

$\large\underline\purple{\bold{Solution :- }}$

Given

• Hypotenuse of a triangle = 10 m

• Base of a triangle = 6m

So,

• Using Pythagoras Theorem,

$\begin{gathered}{\boxed{\bf{\pink{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}}\end{gathered}$

$\rm :  \implies \: {10}^{2} = {6}^{2} + {(Perpendicular)}^{2}$

$\rm :  \implies \:100 = 36 + {(Perpendicular)}^{2}$

$\rm :  \implies \: {(Perpendicular)}^{2} = 100 - 36$

$\rm :  \implies \: {(Perpendicular)}^{2} = 64$

$\boxed{ \purple{ \: \rm :  \implies \:Perpendicular \: = \: 8 \: m}}$

Now,

• To find area of right angle triangle, use

$\large \boxed{ \pink{ \rm \: Area_{(triangle)} \: = \dfrac{1}{2} \times Base \times Perpendicular}}$

$\rm :  \implies \:Area_{(triangle)} \: = \: \dfrac{1}{2} \times 6 \times 8$

$\large \boxed {\purple{ \rm :  \implies \:Area_{(triangle)} \: = \: 24 \: {m}^{2} }}$

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Additional Information

Properties of a triangle

• A triangle has three sides, three angles, and three vertices.

• The sum of all internal angles of a triangle is always equal to 180°. This is called the angle sum property of a triangle.

• The sum of the length of any two sides of a triangle is greater than the length of the third side.

• The side opposite to the largest angle of a triangle is the largest side.

• Any exterior angle of the triangle is equal to the sum of its interior opposite angles. This is called the exterior angle property of a triangle.

Based on the angle measurement, there are three types of triangles:

• Acute Angled Triangle : A triangle that has all three angles less than 90° is an acute angle triangle.

• Right-Angled Triangle : A triangle that has one angle that measures exactly 90° is a right-angle triangle.

• Obtuse Angled Triangle : triangle that has one angle that measures more than 90° is an obtuse angle triangle.