# How Much Corresponding Base Must be Decreased? If

The height of a triangle is increased by 10%. To retain the original area of the triangle, its corresponding base must be decreased by:

- 73/8%
- 100/11%
- 10%
- 64/7%

**Answer: (2) 100/11%**

**Explanation:-**

Let be the height of a triangle is = h and base is b.

Then, the area of the triangle = bh/2

let be the base is decrease by X%.

According to the question,

bh/2 = ( b – b x X/100) (h + h x 10/100)/2

bh = (100b – bX)(11h)/100 x 10

1000 x bh = 1100bh – 11bhX

1000bh – 1100bh = – 11bhX

– 100bh = – 11bhX

X = 100/11%

Hence, the answer is (2) 100/11%.