Question

For a certain model of a jet plane, aerodynamicsrequires that the tail have the profile of a right-angled triangle with area 7.5m². If the height must be 2m less than the baselength for attachment purposes, calculate the base length of the tail.

Answer 1

The base length of the tail is 5meters.

Let the base length of the right-angled triangle be (b) and the height be (h).

The area (A) of a right-angled triangle is given by the formula:

A = 1/2 × b × h

Given:

Area (A) = 7.5m²

Height is 2m less than base length, h = b -2

We have:

7.5 = 1/2 × b × h

7.5 = 1/2 × b × (b - 2)

Solve for (b):

7.5 = 1/2 × b × (b - 2) {multiply both sides by 2)

15 = b × (b - 2)

15 = b² - 2b

Equate all terms to zero:

b² - 2b - 15 = 0

Factorise to find the values of (b).

The factor of the equation is;

(b - 5)(b + 3) = 0

This gives two possible solutions: (b = 5) or (b = -3).

Since the base length cannot be negative, we discard (b = -3) and chose (b = 5) as the base length of the tail.

Therefore, the base length of the tail is 5meters.