Question

The side of a triangle are in the ratio of 3 ratio 4 ratio 5 if its perimeter is 36
then what is its area

Answer 1

Answer:

The area of triangle is 54 cm². Step-by-step explanation: It is given that the sides of a triangle are in the ratio 3 : 4 : 5.

Step-by-step explanation:

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Answer 2

Given :

The ratio of sides of are in the ratio 3 : 4 : 5 .

Perimeter of is 36 units .

Formulas required :

$perimeter \: \: (p)\: \: = a + b + c$

$semiperimeter \: \: (s)\: \: = \frac{a + b + c}{2}$

$area \: \: of \: \: triangle \: \: = \sqrt{s(s - a)(s - b)(s - c)}$

Solution :

Let the common ratio be " k " .

Therefore ,,,

The sides of the are : a = 3k

b = 4k

c = 5k

Perimeter ( p ) = a + b + c

36 = 3k + 4k + 5k

36 = 12k

k = 36 / 12

k = 3

a = 3k = 3 × 3 = 9 units

b = 4k = 4 × 3 = 12 units

c = 5k = 5 × 3 = 15 units

$s \: = \frac{a + b+ c}{2} \\ \\ \: \: = \frac{36}{2} \\ \\ s \: = 18$

$area \: \: of \: \: triangle \: = \sqrt{s(s - a)(s - b)(s - c)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{18(18 - 9)(18 - 12)(18 - 15)} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{18 \times 9 \times 6 \times 3} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \sqrt{18 \times 9 \times 18} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = { \sqrt{18} }^{2} \times \sqrt{9} \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 18 \times 3 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 54 \: \: sq.units$

Area of = 54 sq. units

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