Question

A school is painting its logo in the shape of a triangle in the middle of its sports field. The school wants the height of the triangle to be 6 feet. The area of the logo must be at most 15 square feet. Write an inequality that describes the possible base lengths (in feet) of the triangle.

Answer 1

Answer: $b\leq5$

Step-by-step explanation:

We know that the area of a triangle is given by :-

$\text{A}=\dfrac{1}{2}\times Base\times Height$

Let b be the base (in feet)  of the triangle .

it is given that  , The school wants the height of the triangle to be 6 feet.

Then, the area of triangle will be :-

$\text{A}=\dfrac{1}{2}\times b\times 6=3b$            (1)

The area of the logo must be at most (less than or equal to) 15 square feet.

i.e. Area ≤ 15 square feet         (2)

Now, Substitute the value of A from (1) into (2) , we get

$3b\leq15$

Divide both sides by 3  , we get

$b\leq5$

Hence, the inequality that describes the possible base lengths (in feet) of the triangle :

$b\leq5$