Question

If height of a triangle is increased by 5% and the base is increased by 7%, by what percentage would the area increase?

Answer 1

12.35 % will be change in area.

Answer 2

Answer:

12.35%

Given,

increase in height of a triangle = 5%

increase in base of a triangle = 7%

To find,

percentage increase in area of the triangle.

Solution,

Let the initial height and initial base be 100 cm each.

Area of triangle = 0.5 × base × height

so, initial area = 0.5 × 100 × 100 = 5000 cm²

now, we increase the height and base by 5% and 7% each

therefore,

new height = 105 cm

new base = 107 cm

Let the new area be X.

X = 0.5 × new base × new height

X = 0.5 × 105 × 107

X = 5617.5 cm²

Let the percentage change be Y.

Y = (X- initial area) ÷ X × 100

Y= 5617.5 - 5000 × 100

Y= 12.35 %

Therefore, percentage increase in the area would the be 12.35%.

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