Question

1. A toy manufactor needs a piece of plastic in the shape of a right triangle with the longer leg 1 cm more than the shorter leg. How long should the sides of the triangle be?

a^2+b^2=c^2
x^2+(x+1)^2=(x+2)^2
x^2+x^2+2x+1= x^2+4x+4

2. Martha want to buy a rug for a room that is 11 ft wide and 18 ft. long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 144 sq. feet of carpet. What dimesons should the rug have.
(18-2x)(11-2x)=144

3.A point on the ground 60 ft from the base of the tree, the distance to the top of the tree is 4 ft more than 2 twice the height of the tree.Find the height of the tree.
h^2+60^2=(2h+4)^2
h^2+3600=(2h+4)^2
h^2+3600=(2h+4)(2h+4)
h^2+3600= 4h^2+8h+8h+16
h^2+3600=4h^2+16h+16
-h^2 -h^2
3600=3h^2+16h+16
-3600 -3600
0=3h^2+16h-3584

PLEASE HELP ME OUT IF U KNOW A STORTER WAY TO SOLVE THESE PROBLEMS

Answer 1

1. There are an infinte number of solutions, pick any leg, the other leg is 1cm longer. say 34cm, and 35cm.
2. correct, solve for x
3. h^2+60^2=(2h+4)^2
I would use the quadratic equation, I don't see a factor easily.