We know that the base of the triangle is 5 yards more than the height of the triangle
Let base of the triangle be 'b' and height of the triangle be 'h'
⇒ b = h + 5
Also, we have been given that the area of the triangle is 187 square yards
We have to determine the length of the base and height of the triangle.
[tex]Area = \frac{1}{2} * b * h[/tex]
⇒ [tex]Area = \frac{1}{2} * (h+5) * (h)[/tex] = 187
⇒ \frac{1}{2} * (h+5) * (h)[/tex] = 187
⇒ [tex]\frac{h^{2}+5h}{2} = 187[/tex]
⇒ [tex]h^{2}+5h = 187 * 2[/tex]
⇒ [tex]h^{2}+5h - 374 = 0[/tex]
⇒ [tex]h^{2}+22h -17h - 374 = 0[/tex]
⇒ [tex]h (h+22) - 17 (h+22) = 0[/tex]
⇒ [tex] (h-17) (h+22) = 0[/tex]
⇒ h = 17 or h = -22
Since height can't be negative, so h = 17 yards
⇒ b = h + 5 = 17+5 = 22 yards
Hence, height of the triangle is 17 yards and the base is 22 yards.
