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,
[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{x^2}{2}[/tex]
As their sum is 30 less than the number of units in the area of the triangle, so
[tex]\Rightarrow x+x=\dfrac{x^2}{2}-30[/tex]
[tex]\Rightarrow 2x=\dfrac{x^2}{2}-30[/tex]
[tex]\Rightarrow 4x=x^2-60[/tex]
[tex]\Rightarrow x^2-4x-60=0[/tex]
[tex]\Rightarrow x^2-10x+6x-60=0[/tex]
[tex]\Rightarrow x(x-10)+6(x-10)=0[/tex]
[tex]\Rightarrow (x+6)(x-10)=0[/tex]
[tex]\Rightarrow (x+6)=0,(x-10)=0[/tex]
[tex]\Rightarrow x=-6,x=10[/tex]
Neglecting negative roots,
[tex]\Rightarrow x=10[/tex]
Hence, the base and height of the triangle is 10 units, so the area will be,
[tex]\text{Area}=\dfrac{1}{2}\cdot \text{Base}\cdot \text{Height}=\dfrac{1}{2}\cdot 10\cdot 10=50\ unit^2[/tex]
