Matt who stands at 68 inches tall casts an 8 foot shadow at the same time a pear tree casts a 21 foot shadow. How tall is the tree?
since the height:shadow ratio is the same for both,
h/21 = 68/96
a building 16 m tall cost a shadow of 64 m .find the height a building which cost shadow of 16 m the same time
12
To find out the height of the pear tree, we can use a proportion since both Matt's height and his shadow, as well as the tree's shadow, are given. Here's how we can solve it step-by-step:
1. Convert Matt's height from inches to feet. Since there are 12 inches in a foot, divide 68 inches by 12 to get Matt's height in feet: 68 inches / 12 inches/foot = 5.67 feet.
2. Write the proportion between Matt's height and his shadow, and the tree's height and its shadow:
Matt's height / Matt's shadow = Tree's height / Tree's shadow
Substituting the given values:
5.67 feet / 8 feet = Tree's height / 21 feet
3. Now, solve the proportion for the unknown value (Tree's height):
5.67 / 8 = Tree's height / 21
Cross-multiply: 5.67 x 21 = 8 x Tree's height
119.07 = 8 x Tree's height
Divide both sides of the equation by 8: Tree's height = 119.07 / 8
4. Calculate the Tree's height:
Tree's height = 14.88 feet
Therefore, the pear tree is approximately 14.88 feet tall.