The area of a triangular plot, whose sides are 100 m, 105…

The area of a triangular plot, whose sides are 100 m, 105 m and 145 m, is equal to a rectangular field, whose sides are in the ratio 7 : 10. The perimeter (in m) of the rectangular field is?

Show answer & explanation

Correct answer: C

Explanation

The correct answer is Option 3 i.e. $170{\sqrt{3}}$ .

Heron’s Formula : Area of triangle = $\sqrt{s(s-a)(s-b)(s-c)}$

$s = \frac{a + b + c}{2} = \frac{100 + 105 + 145}{2} = \frac{350}{2} = 175$

Area of triangle = $\sqrt{175(175-100)(175-105)(175-145)} = \sqrt{175 \times 75 \times 70 \times 30}$

$= \sqrt{(25^2)(7^2)(3^2)(10^2)} = 25 \times 7 \times 3 \times 10 = 5250$

Let sides of rectangle be 7x and 10x
Area = 70x²= 5250

$x^2 = \frac{5250}{70} = 75$

$x = \sqrt{75} = 5\sqrt{3}$

Perimeter of rectangle = 2 × (7x + 10x) = 34x = $34 \times 5\sqrt{3} = 170\sqrt{3}$ m

SSC Selection Post 2022 PYQ — Question 66