Let a, b, and c denote the lengths of the sides of a right triangle, with c being the length of the hypotenuse. Find the missing sidelength in each of the following cases:
(i) a = 5, b = 7
(ii) a = 8, b = 12
(iii) a = 9, c = 15
(iv) a = 7, b = 12
(v) a = 1.5, b = 3.5

Question

Bright Tutorials · Accepted Answer

Here, c
2
= a
2
+ b
2
(i) Now, c
2
= 5
2
+ 7
2
= 25 + 49
= 74
⇒ c = √74
(ii) Now, c
2
= 8
2
+ 12
2
= 64 + 144
= 208
⇒ c = √208
= $\sqrt{2 \times 2 \times 2 \times 2 \times 13}$
= 4√13
(iii) Here, 15
2
= 9
2
+ b
2
b
2
= 15
2
– 9
2
= 225 – 81
= 144
⇒ b = √144
= $\sqrt{2 \times 2 \times 2 \times 2 \times 3 \times 3}$
= 12
(iv) c
2
= 7
2
+ 12
2
= 49 + 144
= 193
⇒ c = √193
(v) c
2
= 1.5
2
+ 3.5
2
= 2.25 + 12.25
= 14.5
⇒ c = √14.5
2.5 Right-Triangles Having Integer Sidelengths
Figure It Out (Page 50)

The Baudhayana-Pythagoras Theorem — Question 4