S.chand publication New Learning Composite mathematics solution of class 7 Chapter 10 Properties of Triangles Exercise 10E

 Exercise 10E

Question 1

Use Pythagoras theorem to find out , if each triangle is right angled

(a) (26)²=676

(24)²+(10)²

=576+100

=676

Ans : Yes, it is a right angled triangle

(b) (34)²=1156

(30)²+(16)²

=900+256

=1156

Ans : Yes, this triangle is right angled

(c) (12)²=144

=(8)²+(6)²

=64+36

Ans : No, this triangle is not right angled

(d) (61)²=3721

=(60)²+(11)²

=3600+121

=3721

Ans : Yes, this triangle is right angled

(e) (25)²=625

=(18)²+(15)²

=324+225
=549

Ans : No, it is not a right angle triangle

(f) (18)²=324

=(9)²+(14)²

=81+196

=277

Ans : No , it is not a right angled triangle

(g) (41)²=1681

=(40)²+(9)²

=1600+81
=1681

Ans : Yes, it is a right angle triangle

(h) (17)²=289

=(15)²+(8)²

=225+64
=289

Ans : Yes, this triangle is right angled

Question 2

Classify the triangle as acute, obtuse or right. Measures of sides of all triangles are in the same unit.

(a) 8, 11, 13

Sol :

(13²)=169

=(8)²+(11)²

=64+121

=185

Ans : 13²<(8²+10²) . So, Δ is acute angled

(b) 9, 11, 15

Sol :

(15²)=225

=(9²)+(11²)

=81+121

=202

Ans : 15²<(9²+11²) . So, Δ is obtuse angled

(c) 9, 40, 41

Sol :

(41²)=1681

=(9²)+(40²)

=81+1600

=1681

Ans : 41²<(9²+40²) . So, Δ is obtuse angled

(d) 7, 10, 12

Sol :

(12)²=144

=(7²)+(10²)

=49+100

=149

Ans : 12²<(7²+10²) . So, Δ is acute angled

(e) 7, 8, 11

Sol :

(11)²=121

=(7²)+(8²)

=49+64

=113

Ans : 11²>(7²+8²) . So, Δ is obtuse angled

(f) 10, 24, 26

Sol :

(26)²=676

=(10²)+(24²)

=100+576

As 26²=(10²+24²). So, Δ is right angled

(g) 10, $12\frac{1}{2}$, $7\frac{1}{2}$

Sol :

$\left(12\frac{1}{2}\right)^2=156.25$

$(10)^2+\left(7\frac{1}{2}\right)^2$

=100+56.25

=156.25

As $\left(12\frac{1}{2}\right)^2=10^2+\left(7\frac{1}{2}\right)^2$

So, Δ is right angled

(h) 9, 13, 16

Sol :

16²=256

9²+13²

=81+169

=250

As 16²>(9²+13²), So Δ is obtuse angled

Question 3

Check whether each set of numbers forms a Pythagorean triples. Write Yes or No.

(a) 30, 40, 50

Sol :

=30²+40²

=900+1600

50²=2500

Since, (30²+40²)=50²

Yes, 30,40, 50 form a Pythagorean triples

(b) 15, 36, 39

Sol :

=15²+36²

=225+1296

=1521

39²=1521

Yes, 15,36 and 39 form a Pythagorean triples

(c) 10, 12, 13

Sol :

=10²+12²

=100+144

=244

13²=169

No, 10,12 and 13 don't form a Pythagorean triples

(d) 9, 12, 15

Sol :

15²=225

=9²+12²

=81+144

=225

Yes, 9,12 and 15 form a Pythagorean triples

(e) 10, 15, 17

Sol :

=10²+15²

=100+225

=225

No, 10, 15 and 17 don't form a Pythagorean triples

(f) 9, 14, 19

Sol :

=9²+14²

=81+196

=277

19²=361

No, 9,14 and 19 don't form a Pythagorean triples

(g) 63, 16, 65

Sol :

=63²+16²

=3969+256

=4225

65²=4225

Yes, 63, 16 and 65 form a Pythagorean triples

(h) 64, 48, 80

Sol :

=64²+48²

=4096+2304

=6400

80²=6400

Yes, 64, 48 and 80 form a Pythagorean triples

Question 4

Suppose, the numbers a, b and c form a Pythagorean triplet. Is each of the following, also a Pythagorean triplet? Explain.

(a) A + 1, b + 1, c + 1

Sol :

Suppose a=2, b=4 and c=6

a+1=2+1=3

b+1=4+1=5

c+1=6+1=7

∴(a+1)²+(b+1)²

=3²+5²

=9+25=34

(c+1)²=7²=49

No, They don't form a Pythagorean triplet

(b) 2a, 2b, 2c

Sol :

Suppose, a=3, b=4 and c=5

2a=2×3=6

2b=2×4=8

2c=2×5=10

=(2a)²+(2b)²

=6²+8²

=36+64=100

(2c)²=10²=100

Yes, they form a Pythagorean triplet