Flag problem

[jhanrux]

A FLAG IS BEING MADE WITH A 30x40 unit of rectangle, they decided that it should be separated of 2 equal triangle with 10 unit gap, find the area of the orange region of the flag.

 

[HallsofIvy]

Let the distance from the top right corner of the flag to the point where the red starts be "x". Then each of the triangles is a right triangle with legs of length 30 and 40- x. Use the Pythagorean theorem to find the length of the orange area, in terms of x.

Find the area of each of the two triangles and the orange parallelogram in terms of x. Add those and set them equal to the area of the entire flag, 30(40)= 1200. Solve that equation for x.

 

[jhanrux]

Let the distance from the top right corner of the flag to the point where the red starts be "x". Then each of the triangles is a right triangle with legs of length 30 and 40- x. Use the Pythagorean theorem to find the length of the orange area, in terms of x.

Find the area of each of the two triangles and the orange parallelogram in terms of x. Add those and set them equal to the area of the entire flag, 30(40)= 1200. Solve that equation for x.

how do you find the area of parallelogram in terms of x with just one parallel side given and a height. How do I find the length of base

 

[Deleted member 4993]

how do you find the area of parallelogram in terms of x with just one parallel side given and a height. How do I find the length of base

Each long side of the parallelogram is √[900 + (40-x)²] and the height is 10. So the area is .....

 

[Deleted member 4993]

Another way. Using Halls' "x":
complete a "little" right triangle at one end of the gap:
this triangle will have one leg = 10 and hypotenuse = x.

Let hypotenuse of larger triangles = h.
Then use similar triangles to get: x/10 = h/30 ; h = 3x

Almost done...carry on

Got to admit .... brilliant observation (that too from a hockey-lover)