A ladder that is 14 feet long is placed against a building. The bottom of the ladder is 6 feet from the base of the building.
2 answers:
The first step in solving a problem is illustrating it just as what the picture shows. The ladder represents the hypotenuse, or the longest side of the right triangle. It measures 14 feet. The base measures 6 feet. The height of the top of the ladder from the base of the wall is denoted as x. Since this is a right triangle, the special equations for Pythagorean theorems would apply. The equation is
c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,
14^2 = 6^2 + x^2
x^2 = 14^2 - 6^2
x^2 = 160
x = 4√10 = 12.65 feet
c^2 = a^2 + b^2, where c is the hypotenuse, a and b are the other shorter legs. Substituting the values,
14^2 = 6^2 + x^2
x^2 = 14^2 - 6^2
x^2 = 160
x = 4√10 = 12.65 feet
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Answer:
Step-by-step explanation:
Given
Required
Find the equivalent
We start by changing the / to *
Factorize 10a - 5
Expand 4a² - 1
Express (2a)² - 1² as a difference of two squares
Difference of two squares is such that:
The expression becomes
Combine both fractions to form a single fraction
Divide the numerator and denominator by 2a - 1
Simplify the numerator
Hence,
=