NCERT Class 7 Mathematics Solutions: Chapter 6 –The Triangle and its Properties Exercise 6.5 Part 2

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1. A long ladder reached a window high from the ground on placing it against a wall at a distance. Find the distance of the foot of the ladder from the wall.

A 15 M Long Ladder Reached a Window 12 M High

Answer:

Triangle ABC

Given,

Consider,

In triangle ABC, applying Pythagoras theorem]

[]

So, the distance of the foot of the ladder from the wall is .

2. Which of the following can be the sides of a right triangle?

(i)

(ii)

(iii)

In the case of right-angled triangles, identify the right angles.

Answer:

Triangle ABC

Consider us consider, the larger side be the hypotenuse and also using Pythagoras theorem,

(i) In

L.H.S.

R.H.S.

L.H.S=R.H.S

So, the given sides are of the right angled triangle.

Right angle lies on the opposite to the greater side , i.e., at .

(ii)

In the given triangle,

L.H.S.

R.H.S.

Since, .

So, the given sides are not of the right angled triangle.

(iii)

Triangle PQR

In

L.H.S.

R.H.S.

Since, L.H.S. = R.H.S.

So, the given sides are of the right angled triangle.

Right angle lies on the opposite to the greater side i.e., at .