I need the answer written out in steps

Question

The area of a triangle is 75 square meters. The altitude of the triangle is 5 meters longer than the base of the triangle. Find the base and the altitude of the triangle.

Answer 1

Hi Amy!

The formula for the area of a triangle is A = (1/2)bh

A = area of the triangle

b = the base of the triangle

h = the height, or altitude, of the triangle

Based on your problem, we know that

A = 75

b = this is unknown, so we will just leave it as the variable b

h = this is also unknown, but we do know it is 5 times the base measurement so we can write it as 5b

When we plug these values into the Area equation (A = (1/2)bh) we get

75 = (1/2)(b)(5b)

Solve for b

75*2 = b * 5b

150 = 5b²

(150/5) = b²

30=b²

√(30) = b

Now that we've found the measurement for the base, we can use the relationship we found earlier (h=5b) to find the height.

h = 5b

h = 5√(30)

So the base measurement is √(30) which is approximately 5.48 meters and the altitude is 5√(30) which is approximately 27.39 meters.