Question

Geometry:
Please help and show work! Thank you. :)

1.) The length of a triangle is 7 units more than its width. If the width is doubled and the length is increased by 2, the area is increased by 42 square units. Find the dimensions of the original rectangle.

2.) The side of one square is 2 centimeters longer than the side of the second square. If the sum of their areas is 100cm^2, find the length of the side of each square.

3.) The altitude of a triangle is 5 less than its base. The area of the triangle is 42 square inches. Find its bases and altitude.

Answer 1

Only one question per post.

For #1, I'll give you the first step:
(2x)(x+7+2) = x(x+7) + 42

Solve for x. Try it.

Answer 2

The systems that I have come up with are:

1.) Let l = length
Let w = width

l = w + 7
42 = w^2 + 1 + 2

2.) Let x = side of one square
Let y = side of second square

x = y + 2
x^2 + y ^2 = 100

3.) Let b = base
Let h= height

1/2bh = 42
h = b - 5

Answer 3

2nd and 3rd answers are correct, 1st is not