Answer:
[tex]h= 2x[/tex]
Step-by-step explanation:
Given
Square
[tex]Side = x[/tex]
Triangle
[tex]Base = x[/tex]
[tex]Altitude = h[/tex]
Required
Find h, if both shapes have the same area
The area of the square is:
[tex]Area = x * x[/tex]
[tex]Area = x^2[/tex]
The area of the triangle is:
[tex]Area = \frac{1}{2} * Base*Height[/tex]
[tex]Area = \frac{1}{2} * x*h[/tex]
Equate both areas
[tex]x^2 = \frac{1}{2} * x*h[/tex]
Divide both sides by x
[tex]x = \frac{1}{2} *h[/tex]
Multiply both sides by 2
[tex]2*x = \frac{1}{2} *h*2[/tex]
[tex]2x = h[/tex]
[tex]h= 2x[/tex]
