Question

if the base of a right -angled triangle is 7 cm and the height is 24 cm, what is the length of the hypotenuse of the triangle? 1️⃣ 31 cm 2️⃣ 26 cm 3️⃣ 25 cm 4️⃣ √916 cm

Answer 1

It is said that the base of a right - angled triangle is 7 cm and the height is 24 cm respectively.

★ Have to Find :-

What is the length of the Hypotenuse ?

★ Solution :-

(Hypotenuse)² = (Perpendicular)² + (Base)²

Lets see the concept.

Here we are going to use pythagorean theorem.

☆ What is Pythagorean Theorem ?

According to the Pythagorean theorem also known as ' pythagoras theorem ' states that the square of the length of the hypotenuse is equal to the sum of squares of the base and the perpendicular ( lengths of other two sides ) of the right-angled triangle.

Now,

${\underline{\bf{According \: to \: the \: question}}}$

• Base → 7 cm

• Height which is nothing but Perpendicular → 24 cm

→ (7)² + (24)² = (Hypotenuse)²

→ 49 + 576 = (Hypotenuse)²

→ √625 = Hypotenuse

➹ Hypotenuse = 25 units.

Hence,

Option ( c ) is correct.

Length of the Hypotenuse is 25 units.

Answer 2

Diagram :

$\setlength{\unitlength}{1.5cm}\begin{picture}(6,2)\linethickness{0.5mm}\put(7.7,2.9){\large\sf{A}}\put(7.7,1){\large\sf{B}}\put(10.6,1){\large\sf{C}}\put(8,1){\line(1,0){2.5}}\put(8,1){\line(0,2){1.9}}\qbezier(10.5,1)(10,1.4)(8,2.9)\put(7.1,2){\sf{\large{24}}}\put(9,0.7){\sf{\large{7}}}\put(9.4,1.9){\sf{\large{? }}}\put(8.2,1){\line(0,1){0.2}}\put(8,1.2){\line(3,0){0.2}}\end{picture}$

⠀⠀⠀⠀⠀

$\frak{Given\:} \begin{cases} \sf{Base = 7cm}\\\sf{Perpendicular \:= 24 \:cm}\\\sf{Hypotenuse \:=\:?\: }\end{cases}$⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀

Need To Find : Hypotenuse of Triangle.

⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\bigstar \underline {\bf{ By\:Pythagoras \:Theorem \::}}$⠀⠀⠀

⠀⠀⠀⠀⠀

• $\qquad\qquad:\implies {\sf{ (Hypotenuse)^{2} = (Base)^{2} + (Perpendicular)^{2} }}$

Or ,

$\qquad\qquad:\implies {\sf{ (Hypotenuse)^{2} = (7)^{2} + (24)^{2} }}\\\\\qquad\qquad:\implies {\sf{ 49 + (24)^{2} = (Hypotenuse)^{2} }}\\\\\qquad\qquad:\implies {\sf{ 49 + 576 = (Hypotenuse)^{2} }}\\\\\qquad\qquad:\implies {\sf{ 49 + (24)^{2} = (Hypotenuse)^{2} }}\\\\\qquad\qquad:\implies {\sf{ 625 = (Hypotenuse)^{2} }}\\\\\qquad\qquad:\implies {\sf{ \sqrt{625} = Hypotenuse }}$

⠀⠀⠀⠀⠀$\underline {\boxed{\pink{ \mathrm {  \: \:Hypotenuse \: = 25\: cm}}}}\:\bf{\bigstar}$

⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {  Hence ,\:\:\:Hypotenuse \:of\:Right \:Angled \:Triangle \:is\:\bf{25\:cm}}}}$

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