The area of a right angled triangle is `600c m^2dot` If the base of the triangle exceeds the altitude by 10cm, find the dimensions of the triangle.

Explanation

Let the altitude of the triangle be x cm.
Then, its base `=(x+10)cm.`
Area of the triangle `=(1)/(2)x(x+10)cm^(2).`
`:." "(1)/(2)x(x+10)=600`
`implies" "x(x+10)=1200`
`implies" "x^(2)+10x-1200=0`
`implies" "x^(2)+40x-30x-1200=0`
`implies" "x(x+40)-30(x+40)=0`
`implies" "(x+40)(x-30)=0`
`implies" "x=-40" or "x=30`
`implies" "x=30" "[because" altitude cannot be negative"]`.
Thus, the altitude of the triangle =30 cm.
And, the base of the triangle `=(30+10) cm =40 cm.`