Question

4. The sides of triangle are in ratio of 5:12:13 and its perimeter is 150 cm. The area of triang
O 375 cm2
O 750 cm?
O
250 cm2
O
500 cm2​

Answer 1

Answer:

750 cm² is the answer

Step-by-step explanation:

let the length of sides of triangle be 5x, 12x, 13x.

perimeter = a+b+c

5x+12x+13x = 150

30x = 150

x = 5

5x = 5×5 = 25 cm

12x = 12×5 = 60 cm

13x = 13×5 = 65 cm

s = (a+b+c)/2

s = 150/2 = 75 cm

Area = √s(s-a)(s-b)(s-c)

= √ 75(75-25)(75-60)(75-65)

= √ (75×50×15×10)

= √ 562500

= 750 cm²

Answer 2

⇨ Area = 750cm²

GIVEN

∆'s sides ratio = 5 : 12 : 13

Perimeter = 150 cm

TO FIND

Area of the ∆

CALCULATION

☆ Finding the sides of ∆

Let the 5 = 5n

12 = 12n

13 = 13n

∴ Perimeter according to our assumption = 5n + 12n + 13n = 30n

According to the question perimeter = 150cm

i.e 30n = 150

n = 150 ÷ 30 = 5

∴ n = 5

☆ If n = 5

5n = 5 × 5 = 25 cm

12n = 12 × 5 = 60 cm

13n = 13 × 5 = 65 cm

☆ Finding the area of ∆

According to Pythagoras Theorem

Area of any triangle =

√ s(s-a)(s-b)(s-c) [root for the whole]

where s = semiperimeter & a, b, c are the sides of the triangle .

s = (25 + 60 + 65) ÷ 2 = 150/2 = 75

a = 25

b = 60

c = 65

√ 75 (75-25) (75-60) (75-65)

√ 75 × 50 × 15 × 10

√ 5×5×3×5×5×2×5×3×5×2

5 × 5 × 5 × 3 × 2

750

SOLUTION

Area = 750 cm

HOPE IT HELPS YOU MATE :)

KEEP SMILING