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The side of a triangular field are 32 m, 60 m and 68 m. The area of this field is equal to the area of a rectangular field whose sides are in the ratio 15 : 4. What is the longer side of the rectangular field?

The side of a triangular field are 32 m, 60 m and 68 m. The area of this field is equal to the area of a rectangular field whose sides are in the ratio 15 : 4. What is the longer side of the rectangular field? Correct Answer 60 m

Given:

The side of a triangular field are 32 m, 60 m and 68 m.

The area of this field is equal to the area of a rectangular field whose sides are in the ratio 15: 4

Formula Use:

Area of a triangle when three sides are given: √s(s - a)(s - b)(s - c)

where s is the perimeter s = (a + b + c)/2

Area of rectangle: Length × Breadth

Calculation:

The side of a triangular field are 32 m, 60 m and 68 m.

∴ s = 32 + 30 + 68 / 2 = 80 

Now,

Area of a triangle when three sides are given: √s(s - a)(s - b)(s - c)

⇒ √80(80 - 32)(80 - 30)(80 - 68)

⇒ √921600

⇒ 960 m

Let the sides of the rectangle is 15x and 4x 

∴ Area of rectangle = 15x × 4x = 60x2

Now, 

The area of this field is equal to the area of a rectangular field 

∴ 60x2 = 960 

⇒ x = 4 

∴ The sides of the rectangles are 15x and 4x = 15 × 4, 4 × 4

⇒ The sides of the rectangles are 60m and 16m  

∴ The longer side of the rectangle is 60m 

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