Question

The base of a triangle is 7 inches more than 8 times its height.

The area of the triangle is 435 square inches.
The base is
and the height is

Answer 1

The base and the height of the triangle, given that the base is 7 inches more than 8 times its height is:

• Base is 33.2 inches
• Height is 26.2 inches

How to calculate the base and the height of the triangle?

From the question given, we discovered the following information:

Base of triangle (b) = 7 + height (h)

Area of triangle (A) = 435 square inches

Now, we can calculate the base and height of the triangle as illustrated below:

For height:

A = ½bh

435 = ½ × (7 + h)h

870 = 7h + h²

h² + 7h - 870 = 0

Using formula method, we can obtain h as follow:

• a = 1
• b = 7
• c = -870

`h = (-b\ \pm\ √(b^2\ -\ 4ac))/(2a) \\\\h = (-7\ \pm\ √(7^2\ -\ (4\ *\ 1\ *\ -870))/(2\ *\ 1)\\\\h = (-7\ \pm\ √(49\ +\ 3480))/(2)\\\\h = (-7\ \pm\ √(3529))/(2)\\\\h = (-7\ +\ √(3529))/(2)\ or\ (-7\ -\ √(3529))/(2)\\\\h = 26.2\ or\ -33.2`

Thus, the height is 26.2 inches

For base:

• Base of triangle (b) = 7 + height (h)
• Height (h) = 26.2 inches

b = 7 + h

b = 7 + 26.2

b = 33.2 inches