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

Answer:

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

Step-by-step explanation:

we know that

The area of the triangle is equal to

$A=\frac{1}{2}(b)(h)$

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

$77=\frac{1}{2}(b)(h)$

$154=(b)(h)$ -----> 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

$b=14-3=11\ in$