Question

side of a triangle are in the ratio of 12:17:25 and its perimeter is 540 cm find its area by using herons formula​

Answer 1

Step-by-step explanation:

let a triangle ABC

AB=12x

BC=17x

CA=25x

perimeter= AB+BC+CA

540=12x+17x+25x

29x+25x= 540

54x=540

x=10

AB=12x=12×10 = 120cm

BC=17x=17×10=170cm

CA=25x=25×10=250cm

s=(AB+BC+CA)/2

=540/2

=270cm

Area =√s(s-AB)(s-BC)(s-CA)

=√270×(270-120)×(270-170)×(270-250)

=√270×150×100×20

=√27×10×3×5×10×100×20

=√81×100×100×100

=√9×9 ×10×10×10×10× 10×10

=9×10×10×10

=9000 centimeter square

Answer 2

Answer:

${\pink{\green{\sf{Area\:of\:Triangle=9000cm^{2}}}}}$

Step-by-step explanation:

$\huge{\pink{\green{\underline{\red{\sf{SOLUTION-}}}}}}$

• In the given question Ratio of sides are given and Perimeter is given from these given data we can find the Sides of this Triangle.

• And also Area of this Triangle by Heron's Formula.

$\underline \bold{Given : } \\ \implies Ratio \: of \:Sides = 12 : 17 : 25 \\ \implies Let \: First \: Side = 12x \\ \implies Second \: Side = 17x \\ \implies Third\: Side = 25x \\ \implies Perimeter \: of \: Triangle =540cm \\ \\ \underline \bold{To \: find : } \\ \implies Area \: of \: Triangle = ?$

• According to given question :

$\implies Perimeter \: of \: Triangle = 540 \: cm \\ \implies a + b + c = 540 \\ \implies 12x + 17x + 25x = 540 \\ \implies 54x = 540 \\ \implies x = \frac{540}{54} \\ \bold{\implies x = 10} \\ \\ \bold{ \implies First \: Side = 12x = 12 \times 10 = 120cm} \\ \bold{ \implies Second\: Side = 17x = 17 \times 10 = 170cm} \\ \bold{ \implies Third \: Side = 25x = 25 \times 10 = 250cm}$

• Using Heron's Formula :

$\implies S= \frac{Perimeter }{2} \\ \implies S = \frac{540}{2} \\ \implies S = 270 \\ \\ \underline\bold{by \: Heron's \: Formula : } \\ \implies Area \: of \: Triangle = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies Area = \sqrt{270(270 - 120)(270 - 170)(270 - 250)} \\ \implies Area = \sqrt{270 \times 150 \times 100 \times 20} \\ \implies Area = \sqrt{81000000} \\ \bold{\implies Area = 9000 {cm}^{2} }$