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Question
The area of right -angled triangle is 165 sq meters. Determine its base and altitude if the latter exceeds the former by 7 meters.
Solution
Let the base be x m. Therefore, the altitude will be `(x+7)m`
Area of a triangle =`1/2xx "Base" xx "Altitude"`
∴ `1/2xx x xx(x+7)=165`
⇒` x^2+7x=330`
⇒` x^2+7x-330=0`
⇒`x^2+(22-15)x-330=0`
⇒`x^2+22x-15x-330=0`
⇒`x(x+22)-15(x+22)=0`
⇒`(x+22) (x-15)=0`
⇒` x=-22 or x=15`
The value of x cannot be negative
Therefore, the base is 15 m and the altitude is `{(15+7)=22m}`
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