## Selina Concise Mathematics Class 7 ICSE Solutions Chapter 16 Pythagoras Theorem

**Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 16 Pythagoras Theorem**

### Pythagoras Theorem Exercise 16 – Selina Concise Mathematics Class 7 ICSE Solutions

**Question 1.
**

**Triangle ABC is right-angled at vertex A. Calculate the length of BC, if AB = 18 cm and AC = 24 cm.**

**Solution:**

**Question 2.
**

**Triangle XYZ is right-angled at vertex Z. Calculate the length of YZ, if XY = 13 cm and XZ = 12 cm.**

**Solution:**

**Question 3.
**

**Triangle PQR is right-angled at vertex R. Calculate the length of PR, if:**

**PQ = 34 cm and QR = 33.6 cm.**

**Solution:**

**Question 4.
**

**The sides of a certain triangle are given below. Find, which of them is right-triangle**

**(i) 16 cm, 20 cm and 12 cm**

**(ii) 6 m, 9 m and 13 m**

**Solution:**

**Question 5.
**

**In the given figure, angle BAC = 90°, AC = 400 m and AB = 300 m. Find the length of BC.**

**Solution:**

**Question 6.
**

**In the given figure, angle ACP = ∠BDP = 90°, AC = 12 m, BD = 9 m and PA= PB = 15 m. Find:**

**(i) CP**

**(ii) PD**

**(iii)**

*CD*

**Solution:**

**Question 7.
**

**In triangle PQR, angle Q = 90°, find :**

**(i) PR, if PQ = 8 cm and QR = 6 cm**

**(ii) PQ, if PR = 34 cm and QR = 30 cm**

**Solution:**

**Question 8.
**

**Show that the triangle ABC is a right-angled triangle; if:**

AB = 9 cm, BC = 40 cm and AC = 41 cm

AB = 9 cm, BC = 40 cm and AC = 41 cm

**Solution:**

**Question 9.
**

**In the given figure, angle ACB = 90° = angle ACD. If AB = 10 m, BC = 6 cm and AD = 17 cm, find :**

**(i) AC**

**(ii) CD**

**Solution:
**

**Question 10.
**

**In the given figure, angle ADB = 90°, AC = AB = 26 cm and BD = DC. If the length of AD = 24 cm; find the length of BC.**

**Solution:
**

**Question 11.
**

**In the given figure, AD = 13 cm, BC = 12 cm, AB = 3 cm and angle ACD = angle ABC = 90°. Find the length of DC.**

**Solution:
**

**Question 12.
**

**A ladder, 6.5 m long, rests against a vertical wall. Ifthe foot of the ladcler is 2.5 m from the foot of the wall, find upto how much height does the ladder reach?**

**Solution:**

**Question 13.
**

**A boy first goes 5 m due north and then 12 m due east. Find the distance between the initial and the final position of the boy.**

**Solution:**

**Question 14.
**

**Use the information given in the figure to find the length AD.**

**Solution:
**