Question

a triangle has sides of 1.6cm,3cm and 3.4cm find the area by herons formul​

Answer 1

Step-by-step explanation:

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Answer 2

1st Question :

The perimeter of a triangular field is 450 m and its sides are in the ratio 13:12:5. Find the area of the triangle.

Answer :

Let the ratio be 13x,12x and 5x

Perimeter of triangle = Sum of all its side

➞ 450 m = 13x + 12x + 5x

➞ 450 m = 30x

➞ x = 450 ÷ 30

.°. x = 15 m

Value of 13x :

➞ 13x

➞ 13(15)

➞ 195 m

Value of 12x :

➞ 12x

➞ 12(15)

➞ 180 m

Value of 5x :

➞ 5x

➞ 5(15)

➞ 75 m

_________....

So,now we will use Heron's formula :

$\implies\tt{ \frac{a + b + c}{2} }$

$\implies\tt{ \frac{195 + 180 + 75}{2} }$

$\implies \tt{ \cancel\frac{450}{2} = 225 \: m }$

Area of triangle = $\tt{ \sqrt{s(s - a)(s - b)(s - c)} }$

$\longrightarrow\tt{ \sqrt{225(225 - 195)(225 - 180)(225 - 75)} }$

$\longrightarrow \tt \sqrt{{225(30)(45)(150)}}$

$\longrightarrow \tt{ \sqrt{15 \times 15 \times 15 \times 2 \times 15 \times 3 \times 5 \times 3 \times 5 \times 2} }$

$\longrightarrow \tt{15 \times 15 \times 2 \times 3 \times 5}$

$\longrightarrow \tt{6750 \: m{}^{2}} \green \bigstar$

________...

2nd Question :

A triangle has sides of 1.6 cm,3 cm and 3.4 cm.Find the area.

Answer :

$\implies\tt{ \frac{1.6 + 3 + 3.4}{2} }$

$\implies \tt{ \cancel\frac{8}{2} = 4 \: m }$

$\longrightarrow\tt{ \sqrt{4(4 - 1.6)(4 - 3)(4 - 1.4)} }$

$\longrightarrow \tt \sqrt{{4(2.4)(1)(0.6)}}$

$\longrightarrow \tt{ \sqrt{2 \times 2 \times 6\times 0.4\times 1 \times 0.6 } }$

$\longrightarrow \tt{ \sqrt{5.76} }$

$\longrightarrow \tt{2.4\: cm{}^{2}} \green \bigstar$