Question

Please Help!

The base of a triangle is 3 inches shorter than its height. The area of the triangle is 77 square inches. Find the base and the height

Explain Step-by-step please
I need the work

Answer 1

The base is
`11\ in` and the height is
`14\ in`

Explanation:

we know that

The area of the triangle is equal to

`A=(1)/(2)(b)(h)`

where

b is the base of triangle

h is the height of triangle

In this problem

`b=h-3` ----> equation A

`A=77\ in^(2)`

so

`77=(1)/(2)(b)(h)`

`154=(b)(h)` -----> equation B

Substitute equation A in equation B

`154=(h-3)(h)`

`h^(2)-3h-154=0`

Solve the quadratic equation by graphing

The solution is
`h=14\ in`

see the attached figure

Find the base b

`b=14-3=11\ in`