#1

in the case of a right triangle, the length of the sides (a, b, c) have a ratio of 1 : √3 : 2

let x = length thus, 500 = x + √3x + 2x

500 = 4.73x

x = 105.66 = a 183.0 = b 211.32 = c

with this information, we can calculate the area of the triangle by the formula A =1/2 base x height,

= 1/2 (183 x 105.6) ≈ 9667

500 = 4.73x

x = 105.66 = a 183.0 = b 211.32 = c

with this information, we can calculate the area of the triangle by the formula A =1/2 base x height,

= 1/2 (183 x 105.6) ≈ 9667

#2

the largest rectangle with a perimeter of 160 units will be a square with sides of 40 units, in which case the area will be

L x W = 40 x 40 =1600 units