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Need some help with two algebra questions?
1. A 25 foot ladder is leaning against a house. If the bottom of the ladder is 15ft from the base of the house, how high does the ladder reach?
2. The width of a rectangle is 3m less than the width. The area of the rectangle is 18n^2. Find the lenghth and the width.
Please show me how to solve for both of these. Thank you.
2 Answers
- Jun AgrudaLv 710 years agoFavorite Answer
√(15² + x²) = 25
225 + x² = 625
x² = 400
x = 20
Answer 1: 20 feet
--------------
Length—x:
x(x - 3) = 18
x² - 3x = 18
x² - 1.5x = 18 + (- 1.5)²
x² - 1.5x = 18 + 2.25
(x - 1.5)² = 20.25
x - 1.5 = 4.5
x = 6
Width:
= 6 - 3
= 3
Answer: length, 6 feet; width, 3 feet
- Bob BLv 710 years ago
The 25-foot ladder is the hypotenuse of a right triangle with 15 feet as one side and the height as the other. The formula for a right triangle is:
c^2 = a^2 + b^2 where c is the hypotenuse with a and b as the sides
25^2 = 15*2 + b^2
625 = 225 + b^2
Subtract 225 from both sides:
400 = b^2
b = sqrt(400) = 20 feet
2. The width of a rectangle is 3m less than the width. The area of the rectangle is 18n^2. Find the lenghth and the width.
Use these two equations:
L = W + 3 [width plus 3 meters equals the length]
L * W = 18 [area, length times width, is 18]
Substitute (W + 3) [from equation 1] for L in equation 2:
(W + 3) * W = 18
Multiply out the left side:
W^2 + 3W = 18
Rewrite to quadratic form:
W^2 + 3W - 18 = 0
Factor to:
(W + 6)(W - 3) = 0
Ignore the negative root (width must be positive).
The width is 3 meters and the length (W + 3) is 6 meters.
