NCERT Solutions for Chapter: Triangles, Exercise 1: Exercise

In the figure, $QR=4 \mathrm{cm},RP=8 \mathrm{cm}\text{ and }ST=6 \mathrm{cm}$.

If the perimeter of $∆STU\text{ is }27 \mathrm{cm}$, find the length of $PQ$. Show your steps.

A geologist asked his assistant Annie, if the length of the lake, $PQ$, can be found from the information shown below.

Annie said, "it is possible to find the length of the lake,$PQ$ ."
Is Annie's statement correct? Justify your answer with valid reasons.

In the figure below,$OPQ$  is a triangle with $OP=OQ$. $RS$ is an arc of a circle with centre $O$.

Triangle $OSR$ is similar to triangle $OPQ$.

Is the above statement true or false? Justify your reason 

Looking at the above figure, Hari said that the shortest distance between Town $E$ and Town $F$ is $15$ km.

Is the statement True or False? Justify your answer.

Shown below is a rectangle $PQRS$. $\angle UTQ$ is a right angle.

Which of these is TRUE about $∆UST$ and $∆TRQ$?

Leela has a triangular cabinet that fits under his staircase. There are four parallel shelves as shown below.

The total height of the cabinet is $144 \mathrm{cm}$. What is the maximum height of a book that can stand upright on the bottom-most shelf?

Which of the following are definitely similar to each other?

Some concrete water towers have been built to supply water to the localities nearby. They are usually mounted with a cylindrical tank. A water tower for a locality is 40 m high.

The water tower cast a shadow of 25 m. At the same time, a tree near it casts a shadow of 5 m. What is the height of the tree?