Question

b) A 15m long ladder reached a window 12m high from the ground on placing it against a wall at a distance ‘a’. Find the distance of the foot of the ladder from the wall.

Answer 1

Given:

✰ Length of the ladder = 15 m

✰ Height of the wall from the ground = 12 m

To find:

✠ How far the base of the ladder form the wall?

Solution:

Let's understand the concept first! First we will assume that the base of the ladder is x feet from the wall. We know that 15 m long ladder leans against a wall which means length of ladder is 15 m and height of wall is 12 m from the ground. Like this, we will obtain a right angled triangle, as the ladder and wall form a right angle triangle and by using Pythagoras theorem, we will find the value of x that is the base of the ladder from the wall.

Let AB be the length of the ladder,

BC be the height of the wall from the ground and CA be the base of the ladder from the wall = a

By using Pythagoras theorem,

➤ AB² = BC² + CA²

➤ 15² = 12² + a²

➤ 225 = 144 + a²

➤ a² = 225 - 144

➤ a² = 81

➤ a = √81

➤ a = 9 m

∴ 9 m far the base of the ladder form the wall.

_______________________________

Answer 2

★ The distance of the foot of the ladder from the wall is 9 m.

Step-by-step explanation:

Analysis -

‎ ‎ ‎ ‎ ‎It is given that a ladder of length 15 m is placed against a wall of height 12 m, with a distance of 'a' in the base from the wall to the ladder. We've been asked to find the distance of the base 'a'.

Solution -

‎ ‎ ‎ ‎ ‎According to the analysis, we can say that, there forms a right-angled triangular structure, with points XYZ. Let us assume that XY be the length of the ladder, ZX be the height of the wall and YZ be the base of the ground.

• XY = 15 m
• ZX = 12 m
• YZ = 'a' m

Generally, we use Pythagorean Theorem to find any one of the unknown side in a right-angled triangle. Since we aren't known the measure of side YZ, we can apply this theorem and find out the answer.

$\: \: \: \: \: \: \: \: \: \underline {\boxed{\sf{\pmb{ \pink{(XY)^{2} + (YX)^{2} = (ZX)^{2}}}}}}$

Let's solve the equation by substituting the measures in it!

$\dashrightarrow{ \sf{ {(12)}^{2} + {(a)}^{2} = {(15)}^{2} }} \\ \\ \\ \dashrightarrow{ \sf{144 + {(a)}^{2} = 225 }} \\ \\ \\ \dashrightarrow{ \sf{ {(a)}^{2} = 225 - 144 }} \\ \\ \\ \dashrightarrow{ \sf{ {(a)}^{2} = 81 }} \\ \\ \\ \dashrightarrow{ \sf{a = \sqrt{81} }} \\ \\ \\ \dashrightarrow{ \underline{ \underline{ \sf{ \pmb{ \purple{a = \frak{9 \: m}}}}}}}$

And this is the required answer!

So, let us conclude that the distance of the foot of the ladder from the wall is 9 m.

________________________________________________________