Question

a) A ladder is placed in such a
way that its foot is at distance
of 7 m from a wall and its top
reaches a window 24 m above
the ground. Determine the
length of the ladder.​

Answer 1

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Let AB be the ladder and B be the window.

Then,

BC = 24 m and AC = 7 m.

Since, ∆ABC is a right triangle, right angled at C,

Therefore,

(AB)² = (AC)² + (BC)²

=> AB² = (7)² + (24)²

=> AB² = 7 × 7 + 24 × 24

=> AB² = 49 × 576

=> AB² = 625

Now,

AB × AB = 25 × 25

=> AB = 25

Hence:-

The length of the ladder is 25 m.

Answer 2

We have,

Let the length of ladder=x m

Now, distance between foot of ladder and wall=5m

Height of the window from to ground=12m

∴ By using the hypotenuse theorem

∴x²=(12)²+(5)²

x=√( 144+25)

x= √169

x=13

Length of the ladder is 3m

Hence, this is answer.