Question

A patio is configured from a rectangle with two right triangles of equal size attached at the two ends. The length of the rectangle is . The base of the right triangle is less than the height of the triangle. If the total area of the patio is , determine the base and height of the triangular portions.

Answer 1

The question is not complete! The complete question along with answer and explanation is given below.

Complete Question:

A patio is configured from a rectangle with two right triangles of equal size attached at the two ends. The length of the rectangle is 38 ft. The base of the right triangle is 4 less than the height of the triangle. If the total area of the patio is 1155 ft² , determine the base and height of the triangular portions.

Answer:

height of triangle is 21 ft

base of the triangle is 17 ft

Step-by-step explanation:

Area of patio = 1155 ft²

width of rectangle = 38 ft

Let b = base of triangle  

Let x = height of triangle (it is also the height of rectangle see image)

It is given that the base of the right triangle is 4 less than the height of the triangle, so algebraically  

b = x − 4

Area of patio = area of two triangle + area of rectangle

area of rectangle = height*width

area of rectangle = 38*x

area of two triangle = 2 (1/2*base*height)

area of two triangle = 2 (1/2*(x-4)*x  (2 cancel out each other)

area of two triangle = (x-4)*x

Area of patio = area of two triangle + area of rectangle

1155 = (x-4)*x + 38x

1155 = x² - 4x + 38x

1155 = x² +34x

x² +34x - 1155 = 0

Solving with quadratic formula gives

x = 21 and x = -55 (since height cant be negative discard minus value)

So the height of triangle or rectangle is 21 ft

base of the triangle = b = x − 4  = 21 - 4 = 17 ft