problem solving about triangle and rectangle?!

Question

You have 500 feet of fencing which you want to use to enclose a right triangular area. What is the largest area which you can enclose? (In square feet, enter just the number, no commas)

 

 

 

What is the area of the largest rectangle with a perimeter of 160?

 

 

 

Answer 1

#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

 

#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