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Chapter 10: Q. 140 (page 1196)

An architect is designing a hotel lobby. She wants to have a triangular window looking out to an atrium, with the width of the window 6 feet more than the height. Due to energy restrictions, the area of the window must be 140 square feet. Solve the equation 12h2+3h=140 for h, the height of the window.

Short Answer

Expert verified

Height = 14

Step by step solution

01

Step 1. Given 

12h2+3h=140, width should be 6 feet more then height .

02

Step 2. Solving for height 

Given equation is ,

12h2+3h=140Usingquadraticformula,h=-b卤b2-4ac2aNow,12h2+3h-140=0h=-3卤9-4(12)(-140)2(12)h=-3卤2891h=-3+17,h=-3-17

Now , h = 14 ( neglecting negative value )

03

Step 3. Checking 

Checking for area of window :

h=14,w=h+6=20area=12(h)(w)=12(14)(20)=140

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