S.chand books class 8 maths solution chapter 17 Triangles exercise 17 B

 EXERCISE 17 B


Q1 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 1

Two sides begin , calculate the third side marked by letter in each right angled triangle:




Sol :












Q2 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 2

Calculate the length of the ramp





Sol :










Q3 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 3

Calculate the length of the wire






Sol :










Q4 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 4

Look at the figure at the right. If you walk at the speed of 8 m/sec , how much longer will take you to walk from A to B and then from B to C, then directly from A to C ?





Sol :










Q5 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 5

When the sun is directly overhead , a 4 m rod is held in an inclined position so that its shadow is 3 m long . how much higher is one end of the rod than the other ?

Sol :












Q6 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 6

A tree is broken by the wind as shown n the figure . If the point from where it broke is 5 m above the ground and its top touches the ground at a distance of 12 m from its foot , find the total height of the tree before it broke.







[Hint: CD =AC]

Sol :






Q7 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 7

Two chimneys 18 m and 13 m high stand upright in a ground . If their feet are 12 m apart , then find the distance between their tops.







 [Hint: find AD]

Sol :





Q8 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 8

Determine if a triangle with sides of the given lengths is a right triangle. if the triangle is not right angled say whether it is acute angled or obtuse angled.
(i) 15,20,25
(ii) 10,24,26
(iii) 21,28,35
(iv) 12.6,3.2,13
(v) 4.5,11.7,12.5
(vi) 55,48,73

Sol :












Q9 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 9





(i) Calculate the lengths of
(a) AB

Sol :

In ΔADB, Using Pythagoras theorem

$Hypotenuse^2=Height^2+Base^2$

$AB^2=BD^2+AD^2$

$AB^2={36}^2+{27}^2$

$AB=\sqrt{1296+729}$

$AB=\sqrt{2025}$

AB=45


(b) BC

Sol :

In ΔCDB, Using Pythagoras theorem

$Hypotenuse^2=Height^2+Base^2$

$BC^2=BD^2+DC^2$

$BC^2={36}^2+{48}^2$

$BC=\sqrt{1296+2304}$

$BC=\sqrt{3600}$

BC=60


(ii) Prove the triangle ABC is right angled

Sol :

In ΔABC, Using Pythagoras theorem

$Hypotenuse^2=Height^2+Base^2$

$AC^2=BC^2+AB^2$

${AD+DC}^2=60^2+45^2$

${AD+DC}^2=3600+2025$

${27+48}^2=3600+2025$

${75}^2=5625$

5625=5625

ΔABC satisfies Pythagoras theorem therefore it is a right angled triangle




Q10 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 10

The following problems relate to an isosceles triangle. Recall that if AD is drawn perpendicular to BC, then BD = DC. 







Also AD is the axis of symmetry.
Calculate the lengths marked with letters in figures (i)-(iv)




Sol :




























Q11 | Ex-17B | Class 8| S.Chand | Composite maths | Triangles | Chapter-17 | myhelper


Question 11

Given that √3=1.732 , find the altitude of an equilateral triangle whose one side measures 6 cm .

Sol :




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