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
