Question

a certain shark has triangular teeth with a height that is 1 centimeter shorter than the base. if the area of one tooth is 1 square centimeters, find its base and height.

Answer 1

The Shark's teeth has a base of 2 cm and height of 1 cm.

Step-by-step explanation:

Step 1 :

Given,

the area of the shark's triangular teeth = 1 sq cm

Let b be the base and h be the height of the shark's triangular teeth.

We have the teeth's height is 1 cm short than the base

So  h = b - 1

Step 2 :

Area of Triangle  = ($\frac{1}{2}$) × b × h = 1

Substituting h = b -1

($\frac{1}{2}$) × b × (b-1) = 1

=> b² - b = 2 = > b²-b-2 = 1

Solving for b we have

(b-2)(b+1) = 0

b = 2 or b = -1

Since b is the base , we take the positive value as length/distance cannot be negative.

So b = 2

h = b - 1 = 2 - 1 = 1

h = 1

Step 3 :

Answer :

The Shark's teeth has a base of 2 cm and height of 1 cm.