Question

The length of the base and the height of a triangle are numerically equal. Their sum is 30 less than the number of units in the area of the triangle. Find the area of the triangle.

Answer 1

Answer:

50 sq. units

Step-by-step explanation:

The length of the base and the height of a triangle are numerically equal.

Let us assume that, the length and height as x.

So the area of the triangle will be,

$\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{x^2}{2}$

As their sum is 30 less than the number of units in the area of the triangle, so

$\Rightarrow x+x=\dfrac{x^2}{2}-30$

$\Rightarrow 2x=\dfrac{x^2}{2}-30$

$\Rightarrow 4x=x^2-60$

$\Rightarrow x^2-4x-60=0$

$\Rightarrow x^2-10x+6x-60=0$

$\Rightarrow x(x-10)+6(x-10)=0$

$\Rightarrow (x+6)(x-10)=0$

$\Rightarrow (x+6)=0,(x-10)=0$

$\Rightarrow x=-6,x=10$

Neglecting negative roots,

$\Rightarrow x=10$

Hence, the base and height of the triangle is 10 units, so the area will be,

$\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{1}{2}\cdot 10\cdot 10=50\ unit^2$