State Pythagoras Theorem - Mathematics


State Pythagoras theorem 



The square of the hypotenuse is equal to the sum of the squares of the other two sides. Here, the hypotenuse is the longest side and it’s always opposite the right angle

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Chapter 4: Triangles - Exercises 5


RS Aggarwal Secondary School Class 10 Maths
Chapter 4 Triangles
Exercises 5 | Q 9


Construct a triangle ABC with sides BC = 7 cm, ∠B = 45° and ∠A = 105°. Then construct a triangle whose sides are `3/4` times the corresponding sides of ∆ABC.

The sides of triangle is given below. Determine it is right triangle or not.

a = 9 cm, b = l6 cm and c = 18 cm

Using Pythagoras theorem determine the length of AD in terms of b and c shown in Figure.

Each side of a rhombus is 10 cm. If one of its diagonals is 16 cm find the length of the other diagonal.

Calculate the height of an equilateral triangle each of whose sides measures 12 cm.

In ∆ABC, ∠A is obtuse, PB ⊥ AC and QC ⊥ AB. Prove that:

(i) AB ✕ AQ = AC ✕ AP

(ii) BC2 = (AC ✕ CP + AB ✕ BQ)

In an equilateral ΔABC, AD ⊥ BC, prove that AD2 = 3BD2.

Determine whether the triangle having sides (a − 1) cm, 2`sqrta` cm and (a + 1) cm is a right-angled

A man goes 12m due south and then 35m due west. How far is he from the starting point. 

Find the diagonal of a rectangle whose length is 16 cm and area is 192 ?

Find the side and perimeter of a square whose diagonal is `13sqrt2` cm. 

From given figure, In ∆ABC, AB ⊥ BC, AB = BC then m∠A = ?

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `2sqrt(2)` then l (AB) = ?

From given figure, In ∆ABC, AB ⊥ BC, AB = BC, AC = `5sqrt(2)` , then what is the height of ∆ABC?

Find the height of an equilateral triangle having side 4 cm?

A girl walks 200m towards East and then 150m towards North. The distance of the girl from the starting point is ______.

In a ΔABC, ∠CAB is an obtuse angle. P is the circumcentre of ∆ABC. Prove that ∠CAB – ∠PBC = 90°.


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