3. If sides of the triangle are in the ratio 6:4:5 and its perimeter is 90 on then find the area? Question 3. If sides of the triangle are in theratio 6:4:5 and its perimeter is90 on then find the area? in progress 0 Math Josie 2 months 2021-11-23T04:40:50+00:00 2021-11-23T04:40:50+00:00 2 Answers 0 views 0

## Answers ( )

AnswEr:–• Area of the triangle is 135√7 units.

Given:–• Sides of a triangle are in ratio 6:4:5.

ToFind:–• Area of the triangle.

SoluTion:–Sides of the triangle are in ratio

6:4:5PutxintheratioThen,

Sides are

6x,4x,5xPerimeterofatriangle=sumofallsides.★Accordingtothequestion»6x+4x+5x=90→ 15x = 90

→ x = 90/15

→ x =

6Put the value ofin the ratio.

x6x = 6 × 6 =

364x = 4 × 6 =

245x = 5 × 6 =

30Here,

•= 36

a•= 24

b•= 30

cWe’ve to findof the triangle.

semi–perimeter★Formulaforfindingsemi–perimeter(S)ofthetriangleis»S=a+b+c/2→ S = 36 + 24 + 30 / 2

→ S = 90/2

→ S =

45★Formulaforfindingareaofthetriangleis»√s(s–a)(s–b)(s–c)→ √45 (45 – 36) (45 – 24) (45 – 30)

→ √45 × 9 × 21 × 15

→

135√7unitsHence,theareaofthetriangleis135units.## _____________________

Answer: 357.17 unit sq.Step-by-step explanation:Since the ratio is 6:4:5 , let the sides be 6x , 4x and 5x .therefore, 6x + 4x + 5x = 9015x = 90x = 90÷15x = 6sides are 36 , 24 and 30after finding the sides we will find the area by using the heron’s formulaarea = √s(s-a)(s-b)(s-c)where s = perimeter/2area = √(45)(45-36)(45-24)(45-30)= √45×9×21×15= 45×3√7= 135×2.645= 357.17