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in Perimeter and Area of Plane Figures by (49.2k points)
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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

1 Answer

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Best 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

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