Question

the perimeter of a triangular field is 300 cm and its side are in the ratio 5 ratio 12 ratio 13 find the length of the perpendicular from the opposite vertex to the side whose length is 130centimetre​

Answer 1

Answer:

Step-by-step explanation:

The sides are in the ratio= 5:12:13

Let the sides are 5x, 12x and 13x

perimeter = 300cm

⇒ 5x+12x+13x = 300

⇒ 30x = 300

⇒ x = 300/30 = 10cm

sides are = 5×10, 12×10, 13×10 = 50cm, 120cm, 130cm

Notice that this triangle is right angled triangle with angle opposite to side 130cm as 90°. So side 50cm and 120cm are perpendicular to each other.

Area of triangle= 1/2 × 50 × 120 cm²    -----------------------------(1)

Let the length of perpendicular from vertex to the side whose length is 130 be x.

So area = 1/2 × 130 × x    --------------------------------(2)

From equation (1) and (2)

1/2 × 50 × 120 = 1/2 × 130 × x 

⇒ 50×120 = 130×x

⇒ x = 50×120÷130

⇒ x = 46.15 cm

The length of the perpendicular from the vertex to the side whose length is 130 is 46.15cm

Answer 2

$\huge\underline\mathfrak\pink{Ello}$

$\blue{\bold{\underline{\underline{Given:-}}}}$

Sides a , b, c of the triangle are in the ratio 13 : 12 : 5

Perimeter of a traingle = 450 m

$\red{\bold{\underline{\underline{Given:-}}}}$

Area of the triangle=?

$\green{\bold{\underline{\underline{Solution:-}}}}$

a : b : c= 13 : 12 : 5

let the sides of the triangle be

a = 13x

b = 12x

c = 5x

$perimeter = 450 \\ \\ 13x + 12x + 5x = 450 \\ \\ 30x = 450 \\ \\ x = \frac{450}{30} \\ \\ x = 15$

So, the sides of the traingle are

a = 13×15 =195 m

b = 12×15= 180 m

c = 5×15= 75 m

$it \: is \: given \: that \: perimeter \: = 450 \\ \\ 2s = 450 \\ \\ s = \frac{450}{2} \\ \\ s = 225 \\ \\ area \: = \sqrt{s(s - a)(s - b)(s - c) } \\ \\ area = \sqrt{225(225 - 195)(225 - 180)(225 - 75)} \\ \\ area = \sqrt{ {5}^{6} \times {3}^{6} \times {2}^{2} } \\ \\ area = {5}^{3} \times { 3 }^{3} \times {2}^{2} \\ \\ area = 6750 {m}^{2}$

$\huge\underline\mathfrak\orange{Thanks}$