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Question
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
Solution
Let the base of the right triangle be x meters and the altitude (x + 7) meters Then
According to question,
Areas of the right triangle = 165 m2
And as we know that the area of the right triangle = `1/2xx"base"xx"height"`
`1/2xx x xx(x+7) = 165`
x2 + 7x = 330
x2 + 7x - 330 = 0
x2 - 15x + 22x - 330 = 0
x(x - 15) + 22(x - 15) = 0
(x - 15)(x + 22) = 0
x - 15 = 0
x = 15
or
x + 22 = 0
x = -22
Since negative value is not possible. So x = 15 m
Therefore the altitude is
= x + 7 = 15 + 7 = 22
Hence, base of the right triangle be 15m and altitude be 22m.
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