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Question

The altitude of a triangle measures 5 centimeters less than its base . The area of the triangle is 42 square centimeters. Find the length of the base and the altitude

Answer 1

You need to use a variable for an unknown length. Let x = the length of the base.

Then what is the length of the altitude in terms of x?

After that, use A = (1/2)(base)(altitude). Substitute the 42, x and the x expression for the altitude.

You will get an equation that you can solve for x.

Then tell what the base and altitude are.

Answer 2

Altitude = Base - 5

Area = (Base x Altitude) / 2

Let A be Altitude and B be Base

42 = B (B - 5) / 2

84 = B² - 5B

B² - 5B - 84 = 0

(B - 12) (B + 7) = 0

B = 12 or B = -7 (base can't be negative)

So Base = 12

Altitude = 12 - 5 = 7