Question

The base of a triangle is 2 cm shorter than its height. The area of the triangle is 12 cm². If the base if the triangle is x cm, show this information as a quadratic equation and hence find the length of its base​

Answer 1

Given:-

• Base of a triangle is 2 cm shorter than its height.

• Area of the triangle is 12 cm².

• Base of Triangle = x cm

To do:-

• Show this information as a quadratic equation and hence find the length of its base.

Formula used:-

• Area of Triangle = $\dfrac{1}{2}×base×height$

• Middle Term Split

Solution:-

According to question,

Base = 2 cm shorter than its height.

Let the height be h.

$⟹ \:x = h - 2$

$⟹ \:h = x+2$ ____ {1}

Now,

Area of Triangle = $\dfrac{1}{2}×base×height$

$⟹\:12 = \dfrac{1}{2}×x×(x+2)$

$⟹\:24 = x²+2x$

$⟹\: x²+2x-24=0$

The Equation formed is $x²+2x-24=0.$

Using Middle Term Split,

$⟹\: x²+(6-4)x-24=0$

$⟹\: x²+6x-4x-24=0$

$⟹\: x(x+6)-4(x+6) =0$

$⟹\: (x+6)(x-4) =0$

$⟹\: x+6=0\:and\:x-4 =0$

$⟹\: x =-6 \:and\:x=4$

We will ignore negative term, So

${\boxed{⟹\:x=4}}$

Hence, the Base of Triangle is 4cm.

Now, putting the value of x in {1}.

$⟹ \:h = x+2$

$⟹ \:h = 4+2$

${\boxed{⟹ \:h = 6}}$

Hence, the Height of Triangle is 6cm.

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