Question

The height of a triangle is two-thirds of its base. The area of the triangle is 192 square Find the dimensions of the triangle.​

Answer 1

Answer:

Area of triangle = 1/2 (base × height)

Given, area of a triangle is 192 sq ins. and its height is 8 ins less than its base.

Then, let base = b, height = b-8

Hence, 1/2 (b)*(b-8) = 192

Above equation; “times 2”,

(b)*(b-8) = 384

b^2 - 8b - 384 = 0

(b+16)(b-24)=0

therefore, b = -16, or 24

Substitute, b = 24 into

1/2 (b)*(b-8) = (1/2)*(24)*(24–8) =

(1/2)*(24)*(16) = 192 Q.E.D.

Answer 2

Answer:

$let \: base \: = x$

$height = \frac{2}{3} of \: base$

$height = \frac{2}{3} \times x = \frac{2}{3}$

$area of \: triangle = \frac{1}{2} \times b \times h$

$192 = \frac{1}{2} \times x \times \frac{3}{2}x$

$192 = \frac{3}{4} {x}^{2}$

$192 \times 4 = 3x$

$765 = 3x$

$x = \frac{768}{3}$

$x = 256 \: cm$

Hope it helps u ☺️

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