Answer:
8 cm and 13 cm
Step-by-step explanation:
The formula to calculate the area (A) of a triangle is
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
let height = h then base = h + 5 ( base is 5 cm wider than it is tall ), hence
A = [tex]\frac{1}{2}[/tex] h(h + 5) = 52
multiply both sides by 2
h(h + 5) = 104 ( rearrange into standard form )
h² + 5h - 104 = 0 ← in standard form
(h + 13)(h - 8) = 0 ← in factored form
equate each factor to zero and solve for h
h + 13 = 0 ⇒ h = - 13
h - 8 = 0 ⇒ h = 8
but h > 0 ⇒ h = 8
Thus the height = 8 cm and base = 8 + 5 = 13 cm
