NCERT Class 7 Mathematics Solutions: Chapter 6 – the Triangle and Its Properties Exercise 6.5 Part 2 (For CBSE, ICSE, IAS, NET, NRA 2022)

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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 .