Question

Minister of a state went to city Q from city P. There is a route via city R such that PR ⊥ RQ. PR = 2x km and RQ = 2(x + 7) km. He noticed that there is a proposal to construct a 26 km highway that directly connects the two cities P and Q. Based on the above information, answer the following questions.

i) Which concept can be used to get the value of x?
a) Thales Theorem, b) Pythagoras Theorem, c) Converse of Thales Theorem, d) Converse of Pythagoras Theorem

ii) The value of x is
a) 4, b) 6, c)5, d)8

iii) The value of PR is
a) 10km, b) 20km, c) 15km, d) 25km

iv) The value of PQ is
a) 12km, b) 24km, c) 16km, d) 20km

v) How much distance will be saved in reaching city Q after the construction of the highway?
a) 10km, b) 9km, c) 4km, d) 8km

Answer 1

Answer:

i) Pythagoras theorem

ii)5

iii)10km

iv) 18km

v) 4km

Answer 2

Answer:

(i) Which concept can be used to get the value of x?

(a) Thales theorem (b) Pythagoras theorem

(c) Converse of Thales theorem (d) Converse of Pythagoras

theorem

Answer: (b) Pythagoras theorem

(ii) The value of x is

(a) 4 (b) 6 (c) 5 (d) 8

Answer: (c) 5

(iii) The value of PR is

(a) 10 km (b) 20 km (c) 15 km (d) 25 km

Answer:(a) 10 km

(iv) The value of RQ is

(a) 12 km (b) 24 km (c) 16 km (d) 20 km

Answer: (b) 24 km