# What Are The Area Unchanged The Height of The Triangle

The base of a triangle is increased by 10%. To keep the area unchanged the height of the triangle is to be decreased by ?

- 100/11%
- 100/9%
- 11%
- 9%

**Answer: (1) 100/11%**

**Explanation:-**

The area of a triangle = base x height/2

Let the height decreased by X %

According to the question,

(base x 110/100) (height [100 – X)/100]/2 = base x height /2

11 base x height(100 – X)/1000 x 2 = base x height/2

11 x (100 – X)/1000 = 1

100 – X = 1000/11

– X = 1000/11 – 100

– X = (1000 – 1100)/11

– X = – 100/11

X = 100/11

Hence, the answer is (1) 100/11%