The area of a triangle varies jointly as its base and altitude. By what percent will the area change if the base is increased by 15% and the altitude decreased by 25%?
The intensity of illumination at a given point is directly proportional to the intensity of the light source and inversely proportional to the square of the distance from the light source. If a desk is properly illuminated by a 74.0 w lamp 8.00 ft from the desk, what size lamp will be needed to provide the same lighting at a distance of 12.0 ft?
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a = 2 (b+c) solve for c
The area of a triangle A varies jointly as the measures of its length of its base B and its altitude h. If a triangle with an area of 30 sq. cm. has a base of 12 cm and an altitude of 5 cm, find the area of a triangle with a base of 8 cm and an altitude of 4 cm
To find the percentage change in the area of the triangle, we need to calculate the change in the area first, and then express it as a percentage of the original area.
Let's denote the original area of the triangle as A. According to the joint variation relationship, the area of a triangle is given by:
A = k * b * h
where A is the area, b is the base, h is the altitude, and k is the constant of variation.
To see how the area changes with the given percentage changes, we can calculate the new area by substituting the new values into the equation. Let's denote the new base as b' and the new altitude as h'.
The new area A' is given by:
A' = k * (b + 15%) * (h - 25%)
Now, let's consider the percentage change in the area. We can express it using the formula:
% change = (A' - A) / A * 100%
Substituting the corresponding values, we have:
% change = (A' - A) / A * 100%
= ( k * (b + 15%) * (h - 25%) - k * b * h ) / (k * b * h) * 100%
Simplifying the equation, we can cancel out the constant of variation k:
% change = ( (b + 15%) * (h - 25%) - b * h ) / (b * h) * 100%
Now we can substitute the given values to calculate the percentage change in the area.