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Elementary Algebra

Lynn Marecek, MaryAnne Anthony-Smith

$Math Studyset Vaia Explanations$ Math

2nd Edition · 1240 pages

ISBN: 9780998625713

Chapter 10: Q 10.77 (page 1200)

Find the dimensions of a triangle whose width is four more than six times its height and has an area of 208 square inches.

Short Answer

Expert verified

Therefore, the Dimension of a triangle ,width is $52 i n c h e s$ and Height is 8 inches.

Step by step solution

01

Given information

The given statement width is four more than six times its height .

Area of a triangle is 208 square inches.

02

Simplification of the equation

h = the height of a triangle.

4 + $6 h$ = the width

208 = Area of a triangle.

Area = $\frac{1}{2} \times b \times h$

208 = $\frac{1}{2} \times (4 + 6 h) (h)$

Simplify

localid="1648572463497" $416 = (4 + 6 h) (h) 416 = 4 h + 6 h^{2} T a k e 2 a s a c o m m o n 3 h^{2} + 2 h - 208 = 0 a = 3, b = 2 a n d c = - 208 U \sin g q u a d r a t i c f o r m u l a h = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a} h = \frac{- 2 \pm \sqrt{2^{2} + 4 (3) (208)}}{2 (3)} h = \frac{- 2 + 50}{6} o r \frac{- 2 - 50}{6} h = \frac{48}{6}, \frac{- 52}{6} h = 8, - 8.6 (n o t p o s s i b l e) b = 4 + 6 (8) = 52$

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