Question

∆ABC ~∆DEF, ∆ABC has a heights of 20 inches, and ∆DEF has a height of 24 inches. What is the ratio of the area of ∆ABC to the area of ∆DEF?

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Answer 1

The ratio of the area of ∆ABC to the area of ∆DEF is 25/36

Explanation:

∆ABC ~∆DEF

∆ABC has a heights of 20 inches, and ∆DEF has a height of 24 inches

The ratio of the height (h1) of ∆ABC to the height (h2) of ∆DEF is:

h1 / h2= (20 inches) / (24 inches)

h1 / h2= 20 / 24

Simplifying the fraction dividing the numerator and the denominator by 4:

h1 / h2= (20/4) / (24/4)

h1 / h2= 5 / 6

The ratio of the area (A1) of ∆ABC to the area (A2) of ∆DEF is:

A1 / A2 = (h1 / h2)^2

A1 / A2 = (5 / 6)^2

A1 / A2 = 5^2 / 6^2

A1 / A2 = 25 / 36