Question

25. Geometry The area of the triangle shown is no more than 10 square inches.

a. Write an inequality that can be used to find x.
b.
Solve the inequality from part a.
C.
4 in.
(2x-3) in.
What is the maximum height of the triangle?

Answer 1

a. Let's denote the base of the triangle as
`b` (which is given as 4 inches) and the height a
`h`. The formula for the area of a triangle is
`A=(1)/(2)`×
`base`×
`height`.

Given that the area
`A` is no more than 10 square inches, we can write the inequality as:

`(1)/(2)`×
`b`×
`h\leq 10`

Since the base
`b` is given as 4 inches, the inequality becomes:

`(1)/(2)`×
`4`×
`h\leq 10`

Simplifying:

`2h\leq 10`

b. Now we can solve for
`h`:

`2h\leq 10`

Divide both sides by 2:

`h\leq 5`

So, the maximum height

ℎ
`\leq 5`

h of the triangle is 5 inches.

c. Given the dimensions of the triangle, which are a base of 4 inches and a height of 5 inches, the maximum height of the triangle is 5 inches. This matches the result obtained from solving the inequality in part B.