Problema Solution
A gardener wants to create a triangular garden in the shape of a right triangle with shortest side length x – 2y ft. and the middle length side
x + 5y ft. What is an algebraic expression for the area of the garden?
Multiply this out and express in simplest correct mathematical form, including units.
Answer provided by our tutors
Draw a right triangle and label the shortest side with (x -2y) and the longer side with (x +5y). Leave the hypotenuse blank.
Because the area of a right triangle is simply 1/2 (base)(height), you can write the area of this triangle as 1/2 ((x +5y)(x -2y)) ft^2.
To simplify, you distribute the inside portion first to get:
1/2 (x^2 -2xy +5xy -10y^2) ft^2
Now combine like terms:
1/2 (x^2 +3xy -10y^2) ft^2
Distribute the 1/2 to get your final answer:
1/2 x^2 + 3/2 xy - 5y^2 ft^2