Question

ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the foot of the wall, find upto how much height does the ladder reach?

Select from the Answers below

8 m 

 

9 m 

 

5 m


​

Answer 1

The correct answer is 8m. I have explained in the attachment.

Answer 2

Answer:

$\huge\mathfrak{\red{Answer}}$

$\rightarrow\small\bf Height \: = \: 8m$

Step-by-step explanation:

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Question:-}}\mid}}}}$

• Ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m from the foot of the wall, find upto how much height does the ladder reach?

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Hint:-}}\mid}}}}$

• We will observe from the figure that the ladder with the wall forms an angle of 90° , that is, ladder and the wall forms a right angled triangle.
• So, we will use the Pythagoras theorem to find the required height.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Pythagoras \ theorem:-}}\mid}}}}$

• In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

$\huge\underline{\overline{\mid{\bold{\blue{\mathcal{Required \ Solution:-}}\mid}}}}$

Given that the ladder is 10m is long that is the Hypotenuse of the formed triangle is 10m

$\mathcal{\green{And}}$

The foot of the ladder is 6m away from the foot of the wall that is the base of the triangle is 6m.

$\mathcal{\green{Now,}}$

We have to find the height that the ladder reach that is, the perpendicular of the right triangle formed.

$\mathcal{\green{Therefore,}}$

Using the Pythagoras theorem we have;

${H}^{2} = {B}^{2} + {P}^{2}$

${10}^{2} = {6}^{2} + {AB}^{2}$

$100 = 36 + {AB}^{2}$

${AB}^{2} = 100 - 36$

${AB}^{2} = 64$

$AB = 8m$

$\fbox{\purple{Height \ is \ 8m}}$

$\mathfrak{\red{ \ \ \ \ \ \ \ \ \ \ \ \ @MissTranquil}}$