NCERT Solutions for Class 9 Math Chapter 12 - Herons Formula

Answer:

(i) Traffic signal board is in the shape of equilateral triangle. Let name it $∆$ABC.
$\therefore$ Side of equilateral triangle ABC = a units (given)
Perimeter of equilateral triangle i.e., 2s = a + a + a = 3a

(ii) Perimeter of this equilateral triangle = 180 cm
$\Rightarrow$ a + a + a= 180 cm
$\Rightarrow$ 3a= 180 cm

Answer:

Let sides of triangular side walls of fly- over in metres are a, b and c.
$\therefore$ a = 122 m, b = 22 m and c = 120 m
Perimeter of triangle,
2s = (122 + 22 + 120) m

Answer:

Sides of coloured triangular wall are 15 m, 11 m and 6 m.
$\therefore$ Perimeter of this triangular wall;
2s = (15 + 11 + 6)m

Answer:

Answer:

Given that the sides of triangle are in the ratio of 12 : 17: 25.
$\therefore$ Let sides of triangle in cm are 12x, 17x and 25x.
Perimeter of triangle =540 cm (given)
$\Rightarrow$ 12x + 17x + 25x=540 cm
$\Rightarrow$ 54x=540 cm

$\Rightarrow$ x =10 cm
Now sides of triangle are
12x = 12 × 10 = 120 cm
17x = 17 × 10 = 170 cm
and 25x = 25 × 10 = 250 cm

Answer:

Perimeter of an isosceles triangle = 30 cm
$\Rightarrow$12 cm + 12 cm + Third side = 30 cm

Answer:

In Fig., if we join
BD, we observe that diagonal BD divides quadrilateral ABCD in two triangles (i) Right triangle BCD and (ii) $∆$ABD.
In rt. $∆$BCD, rt. angle is at C.
Therefore Base; CD = 5 m
and Altitude, BC = 12 m

Area of quadrilateral ABCD
= Area ($∆$BCD) + Area ($∆$ABD)
= 30 m² + 35.4 m²
= (30 + 35.4) m²
= 65.4 m²
Hence, area occupied by the quadrilateral is 65.4 m².

Answer:

Answer:

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Answer:

Let rhombus shaped field be ABCD.
Therefore its each equal side;
AB = BC = CD = DA
= 30 m
and let its longer diagonal AC = 48 m, Diagonal
AC divides the rhombus in two congruent triangles.

(i) $∆$ABC and (ii) $∆$ACD. As we know that area of two congruent triangles are equal.
Therefore area ($∆$ABC) = area ($∆$ACD)
Now it is enough to find the area of $∆$ABC whose sides are AB = BC = 30 m and AC = 48 m Perimeter (2s) of $∆$ABC = (30 + 30 + 48) m
$\Rightarrow$ 2s = 108 m

Answer:

Sides of each of 10 triangular pieces of two different colours are 20 cm, 50 cm and 50 cm.

Answer:

Let ABCD be a square whose each sides is a cm
and; diagonal
AC = BD = 32 cm
In rt. $∆$ABC,

Answer:

Answer:

Let ABCD be a field in the shape of trapezium.
Parallel sides AB = 10 m
and CD = 25 m
and Non-parallel sides; AD = 13 m
and BC = 14 m
Draw BM $\perp$ DC

also draw BE || AD so that ABED is a
parallelogram
$\therefore$ BE = AD = 13 m
and DE = AB = 10 m
Now in $∆$BEC,