Question

The front of a traditional thatched house found in Portugal is the shape of a triangle. Suppose the base of the triangle is 1 m less than its height and the area of the triangle is 15 m^2. Find the height of the triangle. (Hint: Use A = 1/2bh.) How tall is the house? (IN METERS)

Answer 1

Given that the front of a traditional thatched house found in Portugal is the shape of a triangle.

The base of the triangle is 1 m less than its height.

The area of the triangle is 15 m²

We need to determine the height of the triangle.

Height of the triangle:

Let h represent the height of the triangle.

Let b represent the base of the triangle.

Since, it is given that "The base of the triangle is 1 m less than its height", it can be written in equation as,

$b=h-1$

Now, substituting $b=h-1$, $h=h$ and $A=15$ in the area of the triangle formula,

$A=\frac{1}{2}bh$

Thus, we have;

$15=\frac{1}{2}(h-1)h$

Simplifying the terms, we have,

$30=(h-1)h$

$30=h^2-h$

 $0=h^2-h-30$

Factoring the terms, we get;

$0=(h-6)(h+5)$

Equating the terms to zero, we get;

$h=6, h=-5$

Since, h cannot take negative values, then $h=6$

Thus, the height of the triangle is 6.

Hence, the house is 6 meters tall.