Algebra homework

Question

The area of square PQRS is 1250 square feet. TUV and W are the midpoints of PQ, QR, RS and SP respectively. What is the area of square TUVW?

Answer 1

The original square PQRS has an area of 1250 sqare feet.

We can find the length of the side using A = s^2

1250 = s^2

s = 25 times the square root of 2

Since T is the midpoint of PQ, then the length of PT is half of that.

The same is true for the length of PW.

Triangle PTW is an isosceles right triangle.

The side of that triangle times the square root of 2 gives us the length of TW.

So the new square has sides which are (25 times the square root of 2) times one half times the square root of 2. The length is 25 feet.

Now you can find the area of the square TUVW.