Respuesta :
Answer:
Base of Island = 15 m, Height = 8 m
Step-by-step explanation:
Here, let the base of the triangular island = b meters
So, the height of the region = (b-7) m
Area of the island = 60 sq.meters
Now, Area of the Triangle [tex]= \frac{1}{2} \times \textrm{Base x Height}[/tex]
or, [tex]60 m^{2} = \frac{1}{2} \times b \times (b-7)[/tex]
or, 120 = b(b-7)
⇒[tex]b^{2} - 7b - 120 = 0 \implies b^{2} -15b+ 8b -120=0[/tex]
or, b(b-15)+8(b-15) = 0
⇒(b-15)(b+8) = 0
Solving this, we get either b = 15 m , or b = -8m
But as b is the base of the triangle , so b CANNOT BE NEGATIVE.
⇒ b ≠ -8 m
Hence, Base of Island = b = 15 m
and Height = b -7 = 15 - 7 = 8 m
