myhelper: RD Sharma 2020 solution class 9 chapter 17 Heron's Formula VSAQS

RD Sharma 2020 solution class 9 chapter 17 Heron's Formula VSAQS

VSAQS

Page-17.27

Question 1:

Find the area of a triangle whose base and altitude are 5 cm and 4 cm respectively.

Answer 1:

Given, base = 5 cm; height = 4 cm
Area of the triangle = $\frac{1}{2} \times Base \times Height$

Question 2:

Find the area of a triangle whose sides are 3 cm, 4 cm and 5 cm respectively.

Answer 2:

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

, where

Therefore the area of a triangle, say having sides 3 cm, 4 cm and 5 cm is given by

a = 3 cm ; b = 4 cm ; c = 5 cm

Now, area
$= \sqrt{6 (6 - 3) (6 - 4) (6 - 5)} = \sqrt{6 \times 3 \times 2 \times 1} = \sqrt{36} = 6 c m^{2}$

Question 3:

Find the area of an isosceles triangle having the base x cm and one side y cm.

Answer 3:

Let us assume triangle ABC be the given isosceles triangle having sides AB = AC and base BC. The area of a triangle ABC, say A having given sides AB and AC equals to y cm and given base BC equals to x cm is given by

Where,

Base = BC = x cm; Height = $\sqrt{y^{2} - \frac{x^{2}}{4}}$

$A = \frac{1}{2} (B a s e \times H e i g h t) = \frac{1}{2} \times x (\sqrt{y^{2} - \frac{x^{2}}{4}}) = \frac{x}{2} (\sqrt{y^{2} - \frac{x^{2}}{4}})$

Question 4:

Find the area of an equilateral triangle having each side 4 cm.

Answer 4:

Area of an equilateral triangle having each side a cm is given by

Area of the given equilateral triangle having each equal side equal to 4 cm is given by

a = 4 cm

Question 5:

Find the area of an equilateral triangle having each side x cm.

Answer 5:

Area of an equilateral triangle, say A having each side a cm is given by

Area of the given equilateral triangle having each equal side equal to x cm is given by

a = x cm

Question 6:

The perimeter of a triangullar field is 144 m and the ratio of the sides is 3 : 4 : 5. Find the area of the field.

Answer 6:

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

, where,

It is given the sides of a triangular field are in the ratio 3:4:5 and perimeter=144 m

Therefore, a: b: c = 3:4:5

We will assume the sides of triangular field as

Substituting the value of x in, we get sides of the triangle as

Area of a triangular field, say A having sides a, b , c and s as semi-perimeter is given by

Question 7:

Find the area of an equilateral triangle having altitude h cm.

Answer 7:

Altitude of a equilateral triangle, having side a is given by

Substituting the given value of altitude h cm, we get

Area of a equilateral triangle, say A having each side a cm is given by

Area of the given equilateral triangle having each equal side equal to is given by;

Question 8:

Let Δ be the area of a triangle. Find the area of a triangle whose each side is twice the side of the given triangle.

Answer 8:

We are given assumed value is the area of a given triangle ABC

We assume the sides of the given triangle ABC be a, b, c

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

Where,

We take the sides of a new triangle as 2a, 2b, 2c that is twice the sides of previous one

Now, the area of a triangle having sides 2a, 2b, and 2c and as semi-perimeter is given by,

, where

Now,

Question 9:

If each side of a triangle is doubled, the find percentage increase in its area.

Answer 9:

The area of a triangle having sides a, b, c and s as semi-perimeter is given by,

Where,

We take the sides of a new triangle as 2a, 2b, 2c that is twice the sides of previous one

Now, the area of a triangle having sides 2a, 2b, and 2c and as semi-perimeter is given by,

Where,

Now,

Therefore, increase in the area of the triangle

Percentage increase in area

Question 10:

If each side of a equilateral triangle is tripled then what is the percentage increase in the area of the triangle?

Answer 10:

Area of an equilateral triangle having each side a cm is given by

Now, Area of an equilateral triangle, say if each side is tripled is given by

a = 3a

Therefore, increase in area of triangle

Percentage increase in area

RD Sharma 2020 solution class 9 chapter 17 Heron's Formula VSAQS

VSAQS

Question 1:

Answer 1:

Question 2:

Answer 2:

Question 3:

Answer 3:

Question 4:

Answer 4:

Question 5:

Answer 5:

Question 6:

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Question 7:

Answer 7:

Question 8:

Answer 8:

Question 9:

Answer 9:

Question 10:

Answer 10:

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