Chapter 2: Q. 2.121 (page 269)

Use the formula $A = \frac{1}{2} b \times h$ to solve for h : ⓐ when A = 170 andb = 17 ⓑ in general

Short Answer

Expert verified

$a . Thesolutionforthegivenformulaish=20 b . Wecanfindtheheightofatriangle,ifweknowtheareaandbasebyusingtheformuala,h= \frac{2 A}{b}$

Step by step solution

Step 1. Given information

The given formula is $A = \frac{1}{2} b \times h$ .

We have to solve the given eqauation for h : when ⓐ A = 170 and b = 17 ⓑ in general

Step 2. Part(b). Explanation

$\begin{array}{l} Solve:a.WhenA=170andb=17 \\ GivenformulaA= \frac{1}{2} \times b \times h \\ \Rightarrow 170= \frac{1}{2} \times 17 \times h (Substitute) \\ \Rightarrow 2 \times 170=2 \times \frac{1}{2} \times 17 \times h (Multiplybothsidesby2) \\ \Rightarrow 340 = 17 \times h (simplify) \\ \Rightarrow \frac{340}{17} = \frac{17 \times h}{17} (Dividebothsidesby17) \\ \Rightarrow 20 =h(Simplify) \\ Thesolutionforthegivenformulaish=20 \end{array}$

Step 2. Part(b)

$\begin{array}{l} b.Ingeneral \\ GivenformulaA= \frac{1}{2} \times b \times h \\ \Rightarrow 2 \times A= 2 \times \frac{1}{2} \times b \times h (Multiplybothsidesby2toclearthefraction) \\ \Rightarrow 2 A= b \times h (Simplify) \\ \Rightarrow \frac{2 A}{b} = \frac{b \times h}{b} (Dividebothsidesbyb) \\ \Rightarrow \frac{2 A}{b} = h (Simplifyforh) \\ Wecanfindtheheightofatriangle,ifweknowtheareaandbasebyusingtheformuala,h= \frac{2 A}{b} \end{array}$

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Use the formula $A = \frac{1}{2} b \times h$ to solve for h : ⓐ when A = 170 andb = 17 ⓑ in general

Short Answer

Step by step solution

Step 1. Given information

Step 2. Part(b). Explanation

Step 2. Part(b)

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Use the formula $A = \frac{1}{2} b \times h$ to solve for h : ⓐ when A = 170 andb = 17 ⓑ in general