The lengths of all 3 sides of a triangle are increased by 40%. Find the percent increase in the area of the triangle.

Question

The lengths of all 3 sides of a triangle are increased by 40%. Find the percent increase in the area of the triangle.

Answer 1

For two similar figures the ratio of the area is as the square of the scale factor between the two figures.

The scale factor is 140/100 (14/10). Therefore the larger triangle's area is 196/100, or 96% more than the smaller.

Answer 2

form a right triangle where x and y are the legs and z is the hypotenuse

the area is A=0.5xy because the legs are perpendicular

increase the legs by 40%

x becomes 1.4x and y becomes 1.4y

the area is A=(0.5)(1.4x)(1.4y)

A=(0.5)(1.96xy)

A=0.98xy

the area went from 0.5xy to 0.98xy

0.98-0.5=0.48

0.48/0.50=48/50=96/100=96% increase (answer)

suppose the triangle is a 3-4-5 right triangle

A=(1/2)(3)(4)=6 square units

increase 3 and 4 both by 40%

3 becomes 4.2 and 4 becomes 5.6

A=(0.5)(4.2)(5.6)=(0.5)(23.52)=11.76 square units

11.76-6=5.76

5.76/6=576/600=144/150=72/75=24/25=96/100=96% increase