The area of the given field is 3500 m2. AF = 25 m, AG = 50 m, AH = 75

1.	The area of the given field is 3500 m2. AF = 25 m, AG = 50 m, AH = 75 m and AB = 100 m. The rest of the dimensions are shown in the figure. Find the value of x.(a) 17 m (b) 20 m (c) 22 m (d) 25 m
Answer» (b) 20m Total area = Area of Δ AFC + Area of Δ AGD + Area of trapezium FCEH + Area of Δ BGE + Area of Δ DGB = \(\frac12\) x AF x FC + \(\frac12\) x AG x DG + \(\frac12\) x (CF + EH) x HF + \(\frac12\) x BH x HE + \(\frac12\)x BG x DG ⇒ \(\frac12\) x 25 x 20 + \(\frac12\) x 50 x 40 + \(\frac12\) x (20 + x) x 50 + \(\frac12\) x 25 × x + \(\frac12\) x 50 x 40 = 3500 ⇒ 250 + 1000 + (20 + x)25 + 12.5x + 1000 = 3500 ⇒ 2250 + 500 + 25x + 12.5x = 3500 ⇒ 37.5x = 3500 – 2750 = 750 ⇒ x = \(\frac{750}{37.5}\) = 20m

The area of the given field is 3500 m2. AF = 25 m, AG = 50 m, AH = 75 m and AB = 100 m. The rest of the dimensions are shown in the figure. Find the value of x.(a) 17 m (b) 20 m (c) 22 m (d) 25 m

Answer»

(b) 20m

Total area = Area of Δ AFC + Area of Δ AGD + Area of trapezium FCEH + Area of Δ BGE + Area of Δ DGB

= \(\frac12\) x AF x FC + \(\frac12\) x AG x DG + \(\frac12\) x (CF + EH) x HF + \(\frac12\) x BH x HE + \(\frac12\)x BG x DG

⇒ \(\frac12\) x 25 x 20 + \(\frac12\) x 50 x 40 + \(\frac12\) x (20 + x) x 50 + \(\frac12\) x 25 × x + \(\frac12\) x 50 x 40 = 3500

⇒ 250 + 1000 + (20 + x)25 + 12.5x + 1000 = 3500

⇒ 2250 + 500 + 25x + 12.5x = 3500

⇒ 37.5x = 3500 – 2750 = 750

⇒ x = \(\frac{750}{37.5}\) = 20m