Question

A ladder is placed against a wall such that it's foot is at a distance of 2.5m from the wall and its top reaches a window 6m above the ground. Find the length of the ladder.

Answer 1

6.5cm. in the length of the ladder

Answer 2

Given:

• A ladder is placed against a wall such that it's foot is at a distance of 2.5m from the wall and its top reaches a window 6m above the ground.

To find:

• The length of the ladder?

Solution:

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

⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━━━━━━━━

☯ Let AB be the ladder and CA be the wall with the window at A.

⠀⠀⠀⠀⠀⠀⠀

Here,

• BC = 2.5 m
• CA = 6 m

By pythagoras theorem,

⠀⠀⠀⠀⠀⠀⠀

$\star\;{\boxed{\sf{\purple{AB^2 = BC^2 + CA^2}}}}$

$:\implies\sf (2.5)^2 + (6)^2$

$:\implies\sf 42.25$

$:\implies{\boxed{\sf{\pink{AB = 6.5\;}}}}\;\bigstar$

$\therefore\;{\underline{\sf{The\;length\;of\;the\:ladder\;is\; \bf{6.5\;m}.}}}$