Question

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Question
A triangle with area 40 square inches has a height that is four less than six times the width. Find the width and height of the
triangle
Provide your answer below:
width:
inches, height:
inches
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SUBMIT
Math

Answer 1

Given the question, the following are the solution steps to answer the question.

STEP 1: Write the formula for the area of the triangle

`Area=(1)/(2)* base* height`

STEP 2: Represent the statements to get an equation

`\begin{gathered} width=base \\ From\text{ the statement,} \\ six\text{ times of the width}=6w \\ four\text{ less than six times the width }=6w-4 \\ \therefore height=6w-4 \end{gathered}`

STEP 3: Substitute into the formula in step 1

`\begin{gathered} height=6w-4,width=base=w,Area=40in^2 \\ Area=(1)/(2)* w*(6w-4) \\ Area=(w(6w-4))/(2)=(6w^2-4w)/(2)=40 \end{gathered}`

STEP 4: Cross multiply

`\begin{gathered} 6w^2-4w=40*2 \\ 6w^2-4w=80 \\ Subtract\text{ 80 from both sides} \\ 6w^2-4w-80=80-80 \\ 6w^2-4w-80=0 \\ Divide\text{ through by 2, we have:} \\ 3w^2-2w-40=0 \\ By\text{ factorization;} \\ 3w^2-12w+10w-40=0 \\ 3w(w-4)+10(w-4)=0 \\ (w-4)(3w+10)=0 \end{gathered}`

STEP 5: Find the values of w

`\begin{gathered} w-4=0,w=0+4,w=4 \\ 3w+10=0,3w=0-10,3w=-10,w=(-10)/(3) \\ \\ Since\text{ the width cannot be negative, width=4 inches} \end{gathered}`

STEP 6: Find the height

`\begin{gathered} Recall\text{ from step 2:} \\ h=6w-4 \\ Substitute\text{ 4 for w} \\ h=6(4)-4=24-4=20in \end{gathered}`

Hence,

width = 4 inches

height = 20 inches