M L Aggarwal Solutions for Exercise 1: EXERCISE 16.1

If the lengths of the sides of a triangle are in ratio $3 : 4 : 5$ and its perimeter is $48 \mathrm{cm}$. Find its area.

The sides of a triangular plot are in the ratio $3 : 5 : 7$ and its perimeter is $300 \mathrm{m}$. Find its area. Take $\sqrt{3}= 1.732$.

If the area of an isosceles triangle is $60 {\mathrm{cm}}^2$ and the length of each of its equal sides is $13 \mathrm{cm}$, find its base.

The base of a triangular field is $3$ times its height. If cost of cultivating the field at the rate of $₹25$ per $100 {\mathrm{m}}^2$ is $₹60000$. Find its base and height.

A triangular park $ABC$ has sides $120 \mathrm{m}, 80 \mathrm{m} \text{and} 50 \mathrm{m}$. A gardner Dhania has to put a fence around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of $₹20$ per meter leaving a space $3 \mathrm{m}$ wide for a gate on one side .

An umbrella is made by stitching $10$ triangular pieces of cloth of two different colours, each piece measuring $20 \mathrm{cm},50 \mathrm{cm},50 \mathrm{cm}$. How much cloth of each colour is required for umbrella?

$ABC$ is an equilateral triangle with each side of length $10 \mathrm{cm}$. In $∆BCD, \angle D=90°$ and $CD=6 \mathrm{cm}$. Find the area of the shaded regions. Give your answer correct to one decimal point.

$ABC$ is an isosceles right-angled triangle and $DEFG$ is a rectangle. If $AD= AE= 3 \mathrm{cm}$ and $DB= EC=4 \mathrm{cm}$, find the area of the shaded region.