Question

sides of a triangle are in the ratio of 5:7:10 and its perimeter is 40 cm find its area​

Answer 1

Answer

• Area of the triangle is 69.2 m²

Explanation

Given

✭ Sides of triangle are of the ratio 5:7:8

✭ Perimeter = 40 cm

To Find

◈ The area of the triangle?

Solution

Assume the sides of the triangle as 5x, 7x & 8x as it is given that the perimeter is 50 cm then the sum of these will give use the value of x and with that we shall find the size of the side and then use the heron's formula for the are!!

➝ Perimeter = Sum of all sides

➝ 40 = 5x+7x+8x

➝ 40 = 20x

➝ 40/20 = x

➝ x = 2

Then the sides will be,

➝ 5x = 5×2 = 10

➝ 7x = 7×2 = 14

➝ 8x = 8×2 = 16

Semi perimeter

➝ Perimeter/2

➝ 40/2

➝ Semi Perimeter = 20

Heron's Formula

Area(∆) = √{s(s-a)(s-b)(s-c)}

• s = 20
• a = 10
• b = 14
• c = 16

➝ √{20(20-10)(20-14)(20-16)}

➝ √{20×10×6×4}

➝ √4800

➝ Area(∆) = 69.2 m²

Answer 2

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GIVEN:-

Sides of a Triangle are in Ratio of 5:7:10.

Perimeter:- 40 Cm.

TO FIND:-

Area.

SOLUTION:-

1) We Have to Find 'x'.

Perimeter = Sides of Triangle

40 = 5x + 7x + 10x

40 = 22x

40/22 = x

x = 1.8 (0r) 2

5x $\implies$5×2=10

7x$\implies$7×2=14

10x$\implies$10×2=20

2) Semi Perimeter.

$\implies$5x + 7x + 10x / 2

$\implies$10 + 14 + 20 / 2

$\implies$34

3) Heron's Formula.

Let, a = 10, b = 14, c = 20.

Area of Triangle = √s(s-a)(s-b)(s-c)

$\implies$√34×24×20×14

$\implies$√17×2×3×2×2×2×5×2×2×7×2

$\implies$2×2×2√17×2×3×5×7

$\implies$8√3,570

So,

Area of Triangle = 8√3,570 (or) 477.9.

• I Hope it's Helpful My Friend.