Question

3. If the height of a triangle is decreased by 40% and its base is increased by 40%, what will be the percentage change in its area?

Answer 1

Answer:

Decreased by 16%

Step-by-step explanation:

Let the initial height be h and base be b.

Area = 1/2 height base = 0.5 bh

When height = h - 40% h = h - 0.4h = 0.6h and base = b + 40% b = b + 0.4b = 1.4b

Area of ∆ = 1/2 (0.6h)(1.4b) = 0.42 bh

% change = (change)/(initial) × 100%

% = (0.5bh - 0.42bh)/0.5bh x 100%

% = (0.08 bh)/(0.5 bh) x 100%

% = (0.08/0.5) x 100% = 16%

Answer 2

Given :-

If  the height of a triangle is decreased by 40% and its base is increased by 40%,

To Find :-

Percentage change in its area?

Solution :-

Let the base be h and height be h

Height is decreased by 40%

h - 40% of h

h - 40/100 × h

h - 4h/10

10h - 4h/10

6h/10

Base increased by 40%

b + 40% of b

b + 40/100 × b

b + 4/10 × b

b + 4b/10

10b + 4b/10

14b/10

Now

Area = 1/2 × 6h/10 × 14b/10

Area = 1/2 × 0.6h × 1.4b

Area = 0.42bh

Now

Area of old triangle = 1/2 × b × h = 0.5bh

Difference between them = 0.5bh - 0.42bh = 0.08bh

Increase in % = 0.08/0.5 × 100

Increase in % = 16%

[tex][/tex]