Answer:
Base = 32 cm
Height = 25 cm
Step-by-step explanation:
Area of a triangle can be calculated as:
![Area = \frac{1}{2}\times Base \times Height](https://tex.z-dn.net/?f=Area%20%3D%20%5Cfrac%7B1%7D%7B2%7D%5Ctimes%20Base%20%5Ctimes%20Height)
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:
![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](https://tex.z-dn.net/?f=Area%3D%5Cfrac%7B1%7D%7B2%7Dbh%5C%5C%5C%5C%20Area%3D%5Cfrac%7B1%7D%7B2%7D%28h%2B7%29%28h%29%5C%5C%5C%5C%20400%3D%5Cfrac%7B1%7D%7B2%7Dh%28h%2B7%29%5C%5C%5C%5C%20800%3Dh%5E%7B2%7D%2B7h%5C%5C%5C%5C%20h%5E%7B2%7D%2B7h-800%3D0)
This is a quadratic equation which can be solved using a quadratic equation as shown below:
![h=\frac{-7+-\sqrt{49-4(1)(-800)} }{2(1)} \\\\ h=\frac{-7+-57}{2}\\\\h=-32,25](https://tex.z-dn.net/?f=h%3D%5Cfrac%7B-7%2B-%5Csqrt%7B49-4%281%29%28-800%29%7D%20%7D%7B2%281%29%7D%20%5C%5C%5C%5C%20h%3D%5Cfrac%7B-7%2B-57%7D%7B2%7D%5C%5C%5C%5Ch%3D-32%2C25)
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.
Answer: $414
Step-by-step explanation:
Total of books= 72
Cost of each book= $5.75
72(5.75)= $414
Answer:
0.6
Step-by-step explanation:
0.6 = six tenths
percent = per 100
so 0.6 = 60%
38.2!! 10.8 x 2 + 8.3 x 2
42 x 28 = (40 + 2) x (20 + 8) = 40 x 20 + 40 x 8 + 2 x 20 + 2 x 8
= 800 + 320 + 40 + 16