Word Problems on Pythagorean Theorem

Q. A person starts moving in the east direction from his initial position and moved $300$ m. Then, he take his left and moved $400$ m and stopped. Now, from the final position he has to go back to the initial position covering minimum distance.
What is the minimum distance to be covered while returning to the initial position?

1. $300$ m
2. $400$ m
3. $700$ m
4. $500$ m

Q. Two sides of the equilateral triangle are reduced by $5$ cm and $4$ cm and third side of the triangle is increased by $4$ cm to form the right angled triangle. Find the original sides of equilateral triangle ?

1. $25$ cm
2. $26$ cm
3. $1$ cm
4. $29$ cm

Q.

The perimeter of an isosceles triangle is $15.6\mathrm{m}$. Find the lengths of its sides, if the base is $3m$ bigger than a leg.

Q.

Liz starts walking from her house at $O$, she walks 24 m towards west to a point $A$, then takes a sharp turn towards north and walks 7 m before stopping at the bus stop at point $B$ as shown in the diagram. Then, the distance between her house and the bus stop is(in m)

1. 25

Q. A rectangular ground of dimensions $120$ m x $50$ m is to be divided into two equal triangular parts. Wooden fence is used for the partition between the two triangualr parts. Find out the length of wooden fence used?

1. $120$ m
2. $170$ m
3. $100$ m
4. $130$ m

Q. The wall is $21$ m high. Rushkil wants to climb the wall with the help of a ladder whose base is to be placed $20$ m away from the base of the wall. What is the required minimum length of the ladder such that Rushkil can climb the wall easily?

1. $25$ m
2. $27$ m
3. $29$ m
4. $21$ m

Q. A $15m$ long ladder is leaning against the wall of a house, touching the window at a height of $12m$ from the ground. How far is the foot of the ladder from the wall of the house (in $m$)?

1. 9

Q. Find the perimeter of triangle whose two sides are of length $12\sqrt{2}$ m each. The length of the third side is equal to the length of diagonal of square of side $10$m ?

1. $34$ m
2. $34\sqrt{2}$ m
3. $44$ m
4. Cannot be determined.