Question

+ Save & Exit CertifyLesson: 13.7 Applications: Quadratic Equat...ISAIAH COVERTQuestion 6 of 17, Step 1 of 16/21CorrectIncline mats, or triangle mats, are offered with different levels of incline to help gymnasts learn basicmoves. As the name may suggest, two sides of the mat are right triangles. If the height of the mat is21 inches shorter than the length of the mat and the hypotenuse is 6 inches longer than the length ofthe mat, what is the length of the mat?AnswerKeypadKeyboard ShortcutsLength of the mat =inches

Answer 1

Given :

The height of the mat is 21 inches shorter than the length of the mat .

The hypotenuse is 6 inches longer than the length of the mat .

Explanation :

Let the length be x , height be y and hypotenuse be z.

The relation between the sides of the triangles

`\begin{gathered} y=x-21 \\ z=x+6 \end{gathered}`

To find the length of mat , use the pythagoras theorem,

`z^2=x^2+y^2`
`(x+6)^2=x^2+(x-21)^2`
`x^2+36+12x=x^2+x^2+441-42x`
`36+54x=x^2+441`
`x^2-54x+405=0`

Solve the quadratic equation by factoring,

`(x-45)(x-9)=0`
`x=45,9`

Answer

Hence the length of mat is 45 in.

As x=9 in gives negati