Question

An orange triangular warning sign by the side of the road has an area of 266 square inches. The base of the sign is 9 inches longer than the altitude. Find the measurements of the base and altitude.

Answer 1

Answer: the base is 28 inches. The altitude is 9 inches

Step-by-step explanation:

Let h represent the altitude of the sign.

Let b represent the length if the base of the sign.

The warning sign is triangular in shape.

The formula for determining the area of a triangle is expressed as

Area = 1/2bh

The base of the sign is 9 inches longer than the altitude. This means that

b = h + 9

If the area of the sign is 266 square inches, it means that

266 = 1/2 × h(h + 9)

266 × 2 = h(h + 9)

532 = h² + 9h

h² + 9h - 532 = 0

h² + 28h - 19h - 532 = 0

h(h + 28) - 19(h + 28) = 0

h(h + 28) - 19(h + 28) = 0

(h + 28)(h - 19) = 0

h = 19 or h = - 28

Since the height cannot be negative, then h = 19

b = h + 9 = 10 + 9

b = 28