The area of a triangular plot having sides 12 m, 35 m and 37 m is equal to the area of a rectangular field whose sides are in the ratio 7 : 3. The perimeter (in m) of the field is:
Answer & explanation
Correct answer: option 1
We know that,
Area of right angled triangle = \(\frac{1}{2}\) × base × height
Perimeter of rectangle = 2(l + b)
Area of rectangle = (l × b)
We have,
Sides of a triangle = 12 m, 35 m and 37 m
This is a right angled triangle so,
The ratio of area of a rectangular field = 7 : 3
Area of right angled triangle = \(\frac{1}{2}\) × 12 × 35 = 6 × 35 = 210 m2
Area of rectangle = (7a × 3a) = 210
= 21a2 = 210
= a2 = 10
= a = \(\sqrt {10}\) m
Now,
Perimeter of rectangle = 2(7x + 3x)
⇒ 2 × 10x = 2 × 10\(\sqrt {10}\) = 20\(\sqrt {10}\)