Hey there!!
How do we find the area of a triangle?
Ans - Formula = ( 1 / 2 ) ( base ) ( height )
In the question, it states the base exceeds the height by 3 cm
Let's take the height as ' x '
The, the base of the triangle would be ' x + 3 '
It's area = 170 cm²
Let' get this into an equation :
( 1/2 ) ( x ) ( x + 3 ) = 170
... ( x / 2 ) ( x + 3 ) = 170
... ( x² + 3x / 2 ) = 170
Multiplying by 2 on both sides
... x² + 3x = 340
Subtract 340 on both sides
... x² + 3x - 340 = 0
We can write this as
... x² - 17x + 20x - 340 = 0
... x ( x - 17 ) + 20 ( x - 17 ) = 0
... ( x + 20 ) = 0
... ( x - 17 ) = 0
... x = -20
... x = 17
As the value can not be in negatives, we take x as 17
The value of height = 17 cm
The value of the base = 20 cm
Hope my answer helps!!
