Embibe Experts Solutions for Chapter: Triangles, Exercise 1: Exercise

Ravi is $1.82 \mathrm{m}$ tall. He wants to find the height of a tree in his backyard. From the tree's base he walked $12.20 \mathrm{m}$ along the tree's shadow to a position where the end of his shadow exactly overlaps the end of the tree’s shadow. He is now $6.10 \mathrm{m}$ from the end of the shadow. How tall is the tree? Express your answer in metre(m).

Ramu is an architect and he is designing his new two-storeyed building. The top view of his first floor and the second floor are in the form of a triangular shape. He designed the second floor in such a way that it forms an inverted triangle when compared to the first floor and its vertices are on the mid-point of the sides of the first floor. The top view of both the floor is represented in the form of a figure.

Find the ratio of top view areas of both the floor. 

Two poles of heights $3 \mathrm{m}$ and $2 \mathrm{m}$ are erected upright on the ground and ropes are stretched from the top of each to the foot of the other.

The height above the ground at which the ropes cross each other is?

Anish is asked to enlarge the red triangle with scale factor $2$ about a centre of enlargement at $(0,2)$. He draws the blue triangle. Explain why Anish is not correct.

During a solar eclipse, the moon passes between the sun and earth and covers sun almost entirely despite being considerably smaller. Why the moon covers almost all part of the sun during an eclipse. Take diameter of the sun as $d=1400000 \mathrm{km}$

Priya brought a triangular-shaped cake for her brother Rahul on his birthday. Priya wants to keep a portion of the cake for Rahul's friend and distribute the rest to her family.

If $△ABC$ is the triangular cake shown below and Priya cuts the cake along $AD$, where $AD$ is the bisector of $\angle A$,  $BC=10 \mathrm{cm}, BD=6 \mathrm{cm}$and $AC=6 \mathrm{cm}$, then, find the value of $AB$ in $\mathrm{cm}$.

Megha made two similar kites. The diagonal of the bigger kite is $1.5$ times the diagonal of the smaller kite.

In the smaller kite, the two diagonals are: $\mathrm{BD}=40 \mathrm{cm}$ and $\mathrm{AC}=68 \mathrm{cm}$. Find the length of the bigger diagonal of the bigger kite (in $\mathrm{cm}$).

A restaurant serves two sizes of sandwiches in their menu: Large and Extra Large

The sandwiches are in the shapes of equilateral triangles. To make these, the chefs will need two different sizes of breads. 

The Large Size sandwich has an area of $81 {\mathrm{cm}}^2$ and can be made with a bread loaf with side length $12 \mathrm{cm}$.

If the area of the Extra Large Sandwich is $225 {\mathrm{cm}}^2$, then find the length of bread loaf (in $\mathrm{cm}$) which the chef will need to use.