Question

Area of a triangle is 6(x⁴y +xy⁶) sq.units.
If its height is 2xy units, then find its base.​

Answer 1

Solution :

Here , it is given that the area of a triangle is 6( x⁴ y + xy⁶ ) unit square where x and y are arbitrary variables .

The height of this triangle is 2xy units .

We need to find the base .

Here , let us initially assume that the base is a units .

Here only the height is specified ; it has to be the corresponding height perpendicular to the base.

Then the area of the triangle will become ½ ( base ) × ( altitude )

Substituting the given values :

½ a ( 2xy ) = 6x⁴y + 6xy⁶

=> axy = 6x⁴y + 6xy⁶

Taking xy common from the Rhs such that they both cancel out :

=> axy = xy( 6x³ + 6y⁵ )

=> a = 6x³ + 6y⁵ .

Thus , the base of the given triangle comes out to be of length 6x³ + 6y⁵ square units .

This is the required answer .

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