Mathematics
Grade10
Easy
Question
A ladder is leaned against a tree, the height on the tree is 12 units, the ladder is 5units away from the tree, what is the length of the ladder?
- 16
- 15
- 3
- 13
Hint:
In this question, a ladder is leaned against a tree. The height of ladder on tree is 12 unit, and ladder is 5 unit away from the tree. We have to find the length of the ladder . It formed the right angled triangle . We have to find the hypotenuse for the length of ladder , use right angled triangle formula quadratic square root.
The correct answer is: 13
Here we have to find that the length of ladder.
Firstly , we have given that the height of ladder on tree is 12 unit and ladder away from tree is 5 unit.
So, Altitude = 12 unit and Base = 5 unit.
So the length of ladder = hypotenuse (Let x ) .
Here we have right angled triangle , we formula for hypotenuse is:
(Hypotenuse)2 = (Altitude)2 + (Base )2
![x squared equals 12 squared plus 5 squared](data:image/png;base64,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)
Taking square root on both the sides of the equation, we get
![√ left parenthesis x squared right parenthesis equals plus-or-minus √ left parenthesis 12 squared plus 5 squared right parenthesis](data:image/png;base64,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)
![x equals plus-or-minus √ 169](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAFwAAAAUCAYAAAAA5FpZAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAQ3ZOC+gAAAldJREFUeNrtWE1ERFEUfp4kSZuRpEUkGS0SSTKSGEnSIpK0SiRJ2rVKkkhGkjZp2SKSpEUiSVokkqRFIq3SIlokGSOm7/ANr9e98978vSbzPj7m3b9z57vnnnPeM4zCQh/YZPjwDNdgiS+DN2gDN3wZvMMm2OLL4A1Kwask/fXgLHjjsI4c2A74DkbBA7DDNkaez9n/Ce6CtYUm+Dg4laR/CxwD40nGjFHgej6Xg8MUN4Eu8I4HY4JF4Ch4D1YWkuAXFMgJOsEbHG5IAlcabx4Al+2NchJLisEL7PMC8Rys2UgPzsS+JNshF/O/NO0mKyRl2WR1/RFw3WGDTvxrwdfA9gztS0iocjH/EWxWtNcwnv9CN7jC32HwxOOrn47gk+Cppq9I51kp2o8ydu9RuBjDx7AidDwxcZpkL/cQ0xk95gTJ2AGPRE7ndsgLzDR4xLFBxRi5oTNZEDxO0Xp4iCJkCHwAJxRVyikPKcqqpk7n4Qb/RIyxLxOxvAopIsAbGFH0naVYHejsSxlYrWiXzwTPLtYV57hUdYRYN664TBL5kjRXwVd6XgJBlnHZsH9oW9uKmIt1O1l8/EAtNygvCWWMUYF/IngT5w5Y2iKsi7NhX8LGoKI9qPNcGxbtN6SCp2gVuDeFciofcMv8k7QMS1PwYoanUYYwQStthi3jpMjo53iDIssbbJ99sT1NjNpm5ZKPSVOVe+IswcQb5zPcgx0V/B7zwXr7TFFuhpkwvxj3t13mwn+JAP/oHD2txv+ElHvsgy+W0OIjx+hRJE8fOYTJRGbm6wa/Af8coAv2ixibAAAAf3RFWHRNYXRoTUwAPG1hdGggeG1sbnM9Imh0dHA6Ly93d3cudzMub3JnLzE5OTgvTWF0aC9NYXRoTUwiPjxtaT54PC9taT48bW8+PTwvbW8+PG1vPiYjeEIxOzwvbW8+PG1vPiYjeDIyMUE7PC9tbz48bW4+MTY5PC9tbj48L21hdGg+pkCsfQAAAABJRU5ErkJggg==)
![x equals plus-or-minus 13](data:image/png;base64,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)
Since the length of the ladder cannot be negative, x= 13 units.
The correct answer is 13 unit.
In this question, we have ladder which is leaned on tree and that formed a right angled triangle. Just use the right angled triangle property and use quadratic square root formula to find the hypotenuse.