A triangular banner has an area of 30 square feet. If the height of the banner is 5 feet, … — SAT

A triangular banner has an area of $30$ square feet. If the height of the banner is $5$ feet, what is the length, in feet, of the base of the banner?

Answer: 12 feet

The length of the base of the banner is

12

feet.

To find the base of the triangular banner, apply the formula for the area of a triangle:

A = \frac{1}{2} b h

. Substituting

30

for the area

A

and

5

for the height

h

yields

30 = \frac{1}{2} b (5)

, or

30 = 2.5b

. Dividing both sides of the equation by

2.5

gives

b = 12

. Therefore, the length of the base of the banner is

12

feet.

Recall the formula for the area of a triangle.

A = \frac{1}{2} b h

The area of a triangle is equal to half the product of its base and height.

Substitute the given values into the area formula.

30 = \frac{1}{2} \times b \times 5

The problem provides the area (

30

square feet) and the height (

5

feet).

Solve for the base

b

b = 12

Multiply both sides of the equation by

2

to clear the fraction, giving

60 = 5b

. Then, divide both sides by

5

to find that

b = 12

Area of a triangle

Question