Question
If side of a scalene $\triangle$ is doubled then area would be increased by:
✓
Answer
- 300%
Area of triangle with sides a, b, c $(\text{A})=\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
New sides are 2a, 2b and 2c
Then $\text{s}' =\frac{2\text{a}+2\text{b}+2\text{c}}{2}=\text{a}+\text{b}+\text{c}$
$\Rightarrow\text{s}'=2\text{s}\ ...(\text{i})$
New area $=\sqrt{\text{s}'(\text{s}'-2\text{a})(\text{s}'-\text{2b})(\text{s}'-\text{2c})}$
$=\sqrt{2\text{s}(2\text{s}-2\text{a})(2\text{s}-2\text{b})(2\text{s}-2\text{c})}$
$=4\sqrt{\text{s}(\text{s}-\text{a})(\text{s}-\text{b})(\text{s}-\text{c})}$
$=4\text{A}$
Increased area = 4A - A = 3A
% of increased area $=\frac{3\text{A}}{\text{A}}\times100=300\%$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Ordinate of a point is positive in:
$\sqrt{10}\times\sqrt{15}$ is equal to:
→- $5\sqrt6$
- $6\sqrt5$
- $\sqrt{30}$
- $\sqrt{25}$
It is known that if a + b = 4 then a + b - c = 4 - c. The Euclid’s axiom that illustrates this statement is:
x = 5, y = 2 is a solution of the linear equation:
Write the correct answer in the following:
The angles of a triangle are in the ratio 5 : 3 : 7 The triangle is.
The angles of a triangle are in the ratio 5 : 3 : 7 The triangle is.
x co-ordinate is known as:
The rationalisation factor of $\sqrt3,$ is:
→→- $-\sqrt3$
- $\frac{1}{\sqrt3}$
- $2\sqrt3$
- $-2\sqrt3$
The figure formed by joining the mid-points of the adjacent sides of a rectangle is a:
- Rhombus.
- Square.
- Rectangle.
- Parallelogram.
If each side of a $\triangle$ is halved then its perimeter will be decreased by:
→