Answer:
0.5 ft
Step-by-step explanation:
Base = 8 ft and Height = 6 ft
Area of Triangle = 0.5*b*h
Area of Triangle = 0.5*8*6 = 24 sq.ft
To increase the Area by 2 sq.ft so the New Area will be 26 sq.ft
New Area = 0.5*b*(New Height)
26=0.5*8*(New Height)
New Height = 6.5 ft
The Increase in Height = New Height - Old Height = 6.5 - 6 = 0.5 ft
The increase in the height of the triangle which has a base of 8 feet and a height of 6 feet, to increase its area by 2 square feet is 0.5 feet.
The area of a triangle is half the product of its base and its height, that is,
Area = (1/2)*base*height.
We have been asked to find the increase in the height of a triangle with base(b) = 8 feet and height(h) = 6 feet, such that its area increases by 2 square feet.
First, we find the initial area of the triangle,
Area = (1/2)*b*h (1/2)*8*6 = 24 square feet.
New area = initial area + 2 square feet = 24 + 2 = 26 square feet
Let the increase in height be x feet,
∴ New height(h1) = 6+x feet
∴ New area = (1/2)*8*(6+x),
But we know that the new area is 26 square feet, so we equate them to get:
(1/2)*8*(6+x) = 26
or, 4(6+x) = 26
or, 24 + 4x = 26
or, 4x = 26 - 24 = 2
or, x = 2/4 = 0.5
∴ The increase in the height of the triangle which has a base of 8 feet and a height of 6 feet, to increase its area by 2 square feet is 0.5 feet.
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