The base of a right-angle triangle is increased by 60%. How much its height should be decreased to retain the same area?

Correct option is D

Given:

Increase in base = 60%

Formula Used:

Area of triangle =$$\frac{1}{2}\times Base \times Height$$​​

Solution:

Let the base and height of the triangle initially be b and h

Then Area =$$\frac{bh}{2}$$​​

If base is increased by 60%:

Then new base =$$b_1 = b + 60\% \ of \ b = b + 0.6b = 1.6b$$​

Now area remains same, hence

​$$\frac{bh}{2} = \frac{b_1 \times h_1}{2}$$​​

​$$\frac{bh}{2} = \frac{1.6b \times h_1}{2}$$​​

​$$h=1.6h_1$$​​

Now if $$h_1$$​ is the new height, then decrease in height = $$h - h_1$$​​

Percentage Change =$$\frac{h - h_1}{h} \times 100$$​​

​$$= \frac{1.6h_1 - h_1}{1.6h_1} \times 100 = 37.5\%$$ 

Alternative Method:

Successive formula:

$$x +y + \frac{xy}{100}$$​

​$$0 = 60 +y + \frac{60}{y}{100}$$​​

​$$-60 = y + 0.6y$$​​

​$$-60 = 1.6y$$​​

​$$y= \frac{-60}{1.6} = -37.5\%$$​​

Here minus sign indicates decrease