Question

1. The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m, find its area.

2. Measure of each side of an equilateral triangle is 12cm. Find its area. (Use Heron’s Formula)

3. Find the cost of laying grass in a triangular field of 50m, 65m and 65m at the rate of

Rs.7 per m2
.
4. The perimeter of a triangular field is 420m and its sides are in the ratio 6:7:8. Find the area of

the triangular field.

5. Find the area of an equilateral triangle whose side is 2√3 cm.

pls tell correct answer pls step by step for this 5 questions ​

Answer 1

Answer:

1. Let sides be 3x, 5x, 7x.

P=300m

3x+5x+7x=300

15x =300

x=20

Sides are : 3*20=60

5*20=100

7*20=140

2. Side=12 cm

Area =√3/4 a^2

=√3/4 *12*12

=36√3

3.

Answer 2

Answer:

1.)1500$\sqrt{3$; 2.) 36$\sqrt{3$;3.)Rs.10,500.;4.) 2100$\sqrt{15$ 5.) 3cm²

Step-by-step explanation:

1.) let 3:5:7 be 3x,5x,7x.

perimeter=30m,

3x+5x+7x=300=15x=300

x=20

first side=3x=20*3=60m

second side=5x=20*5=100m

third side=7x=20*7=140m

using herons formula

$\sqrt{s(s-a)(s-b)(s-c)$

s=semi-perimeter

a,b,c are sides.

s=300/2=150m.

$\sqrt{150(150-140)(150-60)(150-100)$

=$\sqrt{150(10)(90)(50)$

=$\sqrt{6750000$=$\sqrt{675*100*100$

$100\sqrt{675$=$100*5*3\sqrt{3$=$1500\sqrt{3$m²

2.length of each side =12cm.

area using herons formula mentioned above.

s=36(perimeter)/2=18m.

$\sqrt{18(18-12)(18-12)(18-12)$

$\sqrt{18(6)(6)(6)$

36$\sqrt{3$(as done above).

3.cost of laying grass=area of landmass*price of laying grass.

area using herons formula

$\sqrt{90(40)(25)(25)$

$\sqrt{225*100*100$=$15*100=1500.$

cost=Rs.(1500*7)

=10,500.

4. perimeter=420m

sides=6x+7x+8x=420m

21x=420

x=20

first side=6x=20*6=120.

second side=7x=20*7=140.

third side=8x=20*8=160.

area using herons formula.

s=420/2=210.

$\sqrt{210(90)(70)(50)$

$\sqrt{6615*100*100$

100*3*7$\sqrt{15$

=2100$\sqrt15$.

5.side=2$\sqrt{3}$

perimeter=2$\sqrt{3}$+2$\sqrt{3}$+2$\sqrt{3}$=6$\sqrt{3}$

area using herons formula

s=6$\sqrt{3}$/2=3$\sqrt{3}$

$\sqrt{3\sqrt{3} (1)(1)(1)$

=3cm².

thanks. pls mark me the  brainliest i did much hard work to type it. and all answers are correct.