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प्रश्न
The area of a right triangle is `600cm^2` . If the base of the triangle exceeds the altitude by 10 cm, find the dimensions of the triangle.
उत्तर
Let the altitude of the triangle be x cm
Therefore, the base of the triangle will be `(x+10)cm`
Area of triangle = `1/2x(x+10)=600`
⇒`(x+10)=1200`
⇒ `x^2+10x-1200=0`
⇒`x^2+(40-30)x-1200=0`
⇒`x^2+40x-30x-1200=0`
⇒`x(x+40)-30(x+40)=0`
⇒`(x+40) (x-30)=0`
⇒`x=-40 or x=30`
⇒`x=30` [∵ Altitude cannot be negative]
Thus, the altitude and base of the triangle are 30 cm and `(30 + 10 = 40)` cm, respectively.
`"(Hypotenuse)^2=(Altitude)^2+(Base)^2"`
⇒` "(Hypotenuse)^2=(30)^2(40)^2"`
⇒` "(Hypotenuse)^2=900+1600=2500"`
⇒ `"(Hypotenuse)^2=(50)^2"`
⇒ `"(Hypotenuse)^2=50"`
Thus, the dimensions of the triangle are:
Hypotenuse = 50 cm
Altitude = 30 cm
Base = 40 cm
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