Answer:
Base = 32 cm
Height = 25 cm
Step-by-step explanation:
Area of a triangle can be calculated as:
[tex]Area = \frac{1}{2}\times Base \times Height[/tex]
We are given that the base of triangle exceeds the height by 7 cm. This can be expressed in an equation form as:
Base = Height + 7
Lets use B to represent base and H to represent height
B = H + 7
The equation of area can be stated as:
[tex]Area=\frac{1}{2}bh\\\\ Area=\frac{1}{2}(h+7)(h)\\\\ 400=\frac{1}{2}h(h+7)\\\\ 800=h^{2}+7h\\\\ h^{2}+7h-800=0[/tex]
This is a quadratic equation which can be solved using a quadratic equation as shown below:
[tex]h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25[/tex]
Since the height cannot be negative, we'll consider the positive value only i.e height is equal to 25 cm.
Therefore, the length of base will be 25 + 7 = 32 cm.
