Question

in a rectangle triangle ABC right at B, AB = 7 cm , BC = 24 cm. then length of AC is. 30 cm. 17 cm. 25cm. 19cm​

Answer 1

Given:

• AB = 7 cm
• BC = 24 cm

⠀⠀⠀⠀⠀⠀⠀

To find:

• Length of AC = ?

⠀⠀⠀⠀⠀⠀⠀

Solution:

$\setlength{\unitlength}{1.2cm}\begin{picture}(6,5)\linethickness{.4mm}\put(1,1){\line(1,0){4.5}}\put(1,1){\line(0,1){3.5}}\qbezier(1,4.5)(1,4.5)(5.5,1)\put(0,2.5){\large\bf 7 cm}\put(2.8,.3){\large\bf 24 cm}\put(1.02,1.02){\framebox(0.3,0.3)}\put(.7,4.8){\large\bf A}\put(.8,0.5){\large\bf B}\put(5.8,0.5){\large\bf C}\end{picture}$

⠀⠀⠀⠀⠀⠀⠀

$\sf Given \begin{cases} & \sf{Perpendicular,\;AB = 7\;cm } \\ & \sf{Base\;BC = 24\;cm } \end{cases}$

$\bigstar\;{\underline{\sf{Using\; Pythagoras\; Theorem\;in\; \triangle\;ABC\;:}}}$

$\star\;{\boxed{\sf{\purple{(Hypotenuse)^2 = (Base)^2 + (Perpendicular)^2}}}}$

$:\implies\sf (AC)^2 = (BC)^2 + (AB)^2$

$:\implies\sf (AC)^2 = (24)^2 + (7)^2$

$:\implies\sf (AC)^2 = 576 + 49$

$:\implies\sf (AC)^2 = 625$

$:\implies\sf \sqrt{(AC)^2} = \sqrt{625}$

$:\implies{\boxed{\sf{\pink{AC = 25\;cm}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\; length\;of\;AC\;is\; \bf{25\;cm}.}}}$

━━━━━━━━━━━━━━━━━━━━━━━━━━━

$\qquad\qquad\boxed{\underline{\underline{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}$

• Pythagoras theorem states that the sum of the squares of the lengths of the legs of a right triangle is equal to the square of the length of the hypotenuse.

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

Answer 2

Correct Question-:

• In a rectangle ️ △ABC is a right angled triangle and the right angle is at B, AB = 7 cm , BC = 24 cm. then the length of AC is

1. 30 cm
2. 17 cm
3. 25 cm
4. 19 cm

AnswEr -:

• $\boxed{\sf{\blue{The\:option\:3 \:is \: correct. }}}$
• $\boxed{\sf{\blue{The\:length\:of \:AC\:is = 25\: cm }}}$

Given ,

• △ABC is a right angled triangle.
• The right angle is at B .
• AB = 7 cm
• BC = 24 cm

To Find ,

• The length of AC .

☆ Using Pythagoras theorem in ️ △ ABC

$\boxed{\sf{\purple{ Hypotenuse² = Base² + Perpendicular²}}}$

$\sf{\Rightarrow{\pink{AC² = BC² + AB²}}}$

$\sf{\Rightarrow{\pink{AC² = 24² + 7²}}}$

$\sf{\Rightarrow{\pink{AC² = 576 + 49 }}}$

$\sf{\Rightarrow{\pink{AC² = 625 }}}$

$\sf{\Rightarrow{\pink{AC = \sqrt 625 }}}$

$\sf{\Rightarrow{\pink{AC = 25 cm }}}$

Therefore ,

$\boxed{\sf{\blue{The\:length\:of \:AC\:is = 25\: cm }}}$

Hence ,

$\boxed{\sf{\blue{The\:option\:3 \:is \: correct. }}}$

________________________________________

☆ Let's Explore ....................

• Pythagoras 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 of Right angled triangle.

• $\boxed{\sf{\pink{ Hypotenuse² = Base² + Perpendicular²}}}$