Aright triangle has a height 8 cm more than twice the length
of the base. if the area of the triangle 96 cm², what are the
dimensions of the triangle? .

B = 8cm

H = 24cm

Step-by-step explanation:

H = Height

B = Base

A = Area

A = 1/2 * BH

A height 8 cm more than twice the length

of the base

H = 8 + 2B

The area of the triangle 96 cm²

A = 96

Substitute H in terms of B in the equation.

96 = 1/2 * (8 + 2B) * B

96 = 1/2 * (8B + 2B²)

96 = 4B + B²

Trial and error by finding all the squares below 96

* B = 9, 36 + 81 = 107

* B = 8, 32 + 64 = 98

B = 8, put that into the H equation to find the height.

H = 8 + 2B

H = 8 + 16

H = 24

A = 1/2 * 8 * 24 = 96

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