Question

If the height of a triangle is five inches less than the length of its base, and if the area of the triangle is 52 square inches, find the base and the height.

Answer 1

To find the base and height of the triangle, we can use the formula for the area of a triangle, A = 1/2 * base * height. By substituting the given values into the formula, we can solve for the base and height. In this case, the base of the triangle is 13 inches and the height is 8 inches.

Step-by-step explanation:

To find the base and height of the triangle, we can use the formula for the area of a triangle and the given information. Let's denote the base as x and the height as x-5 (since the height is 5 inches less than the length of the base). The formula for the area of a triangle is A = 1/2 * base * height. We can substitute the given values into this formula and solve for x:

52 = 1/2 * x * (x-5)

104 = x * (x-5)

x^2 - 5x - 104 = 0

Solving this quadratic equation, we find that x = 13 or x = -8. Since the length cannot be negative, the base of the triangle is 13 inches and the height is 8 inches.

Answer 2

Base = 10.4 inches

Height = 5.4 inches

Step-by-step explanation:

Let the length of the base = x

The height of the triangle = x - 5

Area of the triangle = 52

;Area of a triangle = 1/2 × base × height

; 52 = [x(x - 5)]/2

; 104 = x^2 - 5

;Where x = square root of (104 + 5)

; x = 10.4

;The base(x) = 10.4 in

;The height (x - 5) = 10.4 - 5

= 5.4 in