Question

The base of a triangle is increased by 66.6% and the altitude is decreased by 40%, then the change in the area of the triangle is ?

Answer 1

`:. color(maroon)(" there is no change in area of the triangle due to the alteration."`

Explanation:

Let the original base of the triangle be b and height be h.

`"Area of the triangle " = 1/2 b h`

After altering the triangle, `"base " = b_1 = b + b * 66.6% = 1.666 b`

`"sCorresponding change in heifht " h_1 = h - h * 40% = 0.6 h`

`"Area of changed triangle " = A_1 = (1/2) 1.66 b * 0.6 b = 1/2 b h`

`:. color(maroon)(" there is no change in area of the triangle due to the alteration."`

Answer 2

`% "decrease in Area"=0.04%`.

Explanation:

Suppose that the base and altitude of the triangle are `b` and `a`

units, resp.

Then, its area `A=1/2*b*a` sq. unit.

The base `b` is increased by `66.6%`.

`:." the new base"=b+b*66.6/100=1.666b`.

Similarly, the new altitude`=0.6a`.

`:." New Area A'"=1/2(1.666b)(0.6a)=1/2(0.9996)ba` sq.unit.

`:."Decrease in Area"=A-A'=1/2ba-1/2(0.9996)ba`,

`=1/2(0.0004)ba` sq.unit.

`:. % "decrease in Area"={1/2(0.0004)ba}/(1/2*b*a)xx100`,

`=0.04%`.

Answer 3

`"no change"`

Explanation:

`"note that "66.6%~~2/3" and "40%=2/5`

`"original area "=1/2bh`

`"new area with "b=5/3b" and "h=3/5h`

`"new area "=1/2xx5/3bxx3/5h=1/2bh`

`"the area remains unchanged"`