Question

The base of a triangle exceeds its altitude by 2 and the area of triangle is 15 sq.units .this statement can be expressed in terms of the quadratic equation
options are,,
a)x^2+2x=30
b)x^2-2x-15=0
c)2x^2-x=30
d)x^2+2x=15 ​

Answer 1

Given:-

• The base of a triangle exceeds its altitude by 2 and the area of triangle is 15 sq.units.

To Do:-

• Form of quadratic equation on this situation.

Formula Used:-

• ${\boxed{\bf{Area\:of\: Triangle=\dfrac{1}{2}\times Base \times Height}}}$

Solution:-

Let the altitude of the triangle be x.

According to question,

• Base = 2 + x

Using Formula,

$\sf :\implies\:Area\:of\: Triangle=\dfrac{1}{2}\times Base \times Height$

$\sf :\implies\:15=\dfrac{1}{2}\times (2+x) \times x$

$\sf :\implies\:15\times2=x^2+2x$

$\sf :\implies\:x^2+2x=30$

Hence, The quadratic equation on this situation is x² + 2x = 30.

[Option {a} is correct]

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Answer 2

Solution:-

Let the altitude of the triangle be h.

According to question,

• B = 2 + h

$\bf :\implies\:Area\:of\: Triangle=\dfrac{1}{2}\times B \times H$

$\bf :\implies\:15=\dfrac{1}{2}\times (2+h) \times h$

$\bf :\implies\:15\times2=h^2+2h$

$\bf :\implies\:h^2+2h-30=0$

Hence, The quadratic equation on this situation is h² + 2h - 30.

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