Question

Q-Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area.
Ans-25cm true or false​

Answer 1

$\bf\underline{\underline{\purple{SOLUTION:-}}}$

Question

• Sides of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm. Find its area?

Given

• Sides of triangle in ratio 12:17:25
• Perimeter = 540cm

To Calculate

• Area __?

Explanation

Sides Given in ratio 12:17:25

Let Sides are 12x, 17x,25x

${\boxed{\red{\tt{Perimeter = Sum \: of \: all \: Sides }}}}$

Where

perimeter = 540 cm

➥ 540 = 12x+17x+25x

➥ 540 = 54x

➥ x= 540/54

➥ x= 10

Sides are : -

12x = 12×10 = 120cm

17x = 17×10 = 170cm

25x = 25×10 = 250cm

${\boxed{\red{\tt{Semi perimeter = a+b+c /2}}}}$

➥ 120+ 170+250 / 2

➥ 540/2

➥ 270

☆ Using Heron's formula ☆

Area = √S(s-a)(s-b)(s-c)

➥ √270(270-120)(270-170)(270-250)

➥ √270(150)(100)(250)

➥√ 270×150×100×250

➥ √ (27×15×2)(10)⁵

➥√ (27×30)(10)⁵

➥ √(27×3)(10)⁶

➥√(81)×(10)⁶

➥√9²= √10⁶

➥9×(10⁶)½

➥ 9×10³

➥ 9000cm²

$\bf\underline{\underline{\purple{HENCE:-}}}$

• Your answer is False

___________________________________________

$\bf\underline{\underline{\green{Additional\: Information:-}}}$

1) In a right ΔABC

ar(ΔABC ) = 1/2×b×h

2) In an equilateral triangle of side a

i) Height = (√3/2 a) units

ii) Area = ( √3/4 a²) sq. units

iii) perimeter = 3a units

3) For isosceles ΔABC in which AB= AC = a and BC =b

i) Height = √4a²-b² / 2 units

ii) Area = (1/4b √4a²-b² sq. units

iii) perimeter = 2a+b units

_______________________________________________