The perimeter of a triangular field is 240dm If two of its sides are 50 dm , and 78 - Maths - Heron\s Formula

Question

The perimeter of a triangular field is 240dm If two of its
sides are 50 dm , and
78 dm , find the length of the perpendicular on the side of
length 50 dm from the 
opposite vertex Calculate also the cost of watering it as Rs
2 75 per 100 m2

Ankush Jain · Accepted Answer

Let the third side of triangle be x dm Perimeter of triangular field = 240 dm x + 78 + 50 = 240 â‡’x + 128 = 420 â‡’ x = 420 â€“ 128 = 112 dm Therefore, the length of third side of triangle is 112 dm Now, let a = 50 dm , b = 78 dm and c = 112 dm So, Area of $Δ ABC = \sqrt{s (s - a) (s - b) (s - c)}$ , where s is the semi - perimeter of the triangle âˆ´ semi - perimeter of $Δ ABC = \frac{a + b + c}{2}$ â‡’ $s = \frac{78 + 50 + 112}{2} = \frac{240}{2} = 120 cm$ âˆ´ Area of triangle, $Δ A = \sqrt{120 (120 - 78) (120 - 50) (120 - 112)}$ = $\sqrt{120 \times 42 \times 70 \times 8} = 1680 {d m}^{2}$ (1) Also area of triangle = $\frac{1}{2} \times b a s e \times h e i g h t = \frac{1}{2} \times 50 \times h$ (2) Equating (1) and (2), we get $\frac{1}{2} \times 50 \times h = 1680$ â‡’ h = 67 2 dm Area of triangle = 1680 dm2 We know that, 1 dm = 0 1 m So, 1 dm2 = 0 1 Ã— 0 1 m2 = 0 01 m2 Hence, area of triangle = 1680 Ã— 0 01 m2 = 16 8 m2 Given, cost of watering for 100 m2 = Rs 2 75 So, cost of watering for 16 8 m2 = $R s \frac{2 75}{100} \times 16 8 = R s 0 462$

The perimeter of a triangular field is 240dm. If two of its sides are 50 dm , and 78 dm , find the length of the perpendicular on the side of length 50 dm from the opposite vertex. Calculate also the cost of watering it as Rs.2.75 per 100 m2

The perimeter of a triangular field is 240dm. If two of its sides are 50 dm , and

78 dm , find the length of the perpendicular on the side of length 50 dm from the

opposite vertex. Calculate also the cost of watering it as Rs.2.75 per 100 m²