Ratio parts sum to 3 + 5 + 7 = 15, giving sides 60 m, 100 m, and 140 m with semi-perimeter s = 150 m. Area = √(150 x 90 x 50 x 10) = 1500√3 m² (approx 2598.08 ...
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Third side is 32 – (8 + 11) = 13 cm. Semi-perimeter s = 32 / 2 = 16 cm. By Heron’s formula, area = √(16 x (16 – 8) x (16 – 11) x (16 – 13)) = √(16 ...
Dropping perpendiculars splits the difference into two segments of (40 – 20) / 2 = 10 cm. Height is √(26² – 10²) = √(676 – 100) = √576 = 24 cm. Area is (1/2) x (40 + 20) x 24 ...
In rectangle ABCD, base AD = 8 cm and perpendicular height from vertex E to AD is 10 cm. The area of triangle ADE is (1/2) x base x height = (1/2) x 8 x 10 = 40 cm².
Perimeter of a circle is 2 x π x r, directly proportional to radius r. Therefore, the ratio of circumferences C1 / C2 = (2πr1) / (2πr2) = r1 / r2 = 5 / 4, so ratio of radii is ...