Heights and shadows!!!!!

Geometry Level 1

UA 90-foot tall lakefront hotel casts a showdow on the water. How long is the shawdow if a nearby 10-foot tall basketball hoop casts a 7-foot shawdow?


The answer is 63.

Ashtik Mahapatra by Ashtik Mahapatra , 22, India

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4 solutions

Ashtik Mahapatra
Apr 3, 2014

Lett x=length of hotel's shadow Notice there's a relationship between the height of the object and the length of the shadow. So we have this ratio: X/90=7/10 Notice the shadow lengths are the numerators and the denominators are the objects heights. X=7*90/10 X=630/10 X=63 So the length of the hotel's shadow is 63 ft.

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Bharath Spidy
Jul 1, 2014

Length of hotel = 90 foot

Hoop casts = 10 foot

Hoop casts Shadow = 7 foot

so, 3 foot is reducing every 10 foot

ie., shadow: 10 foot - 3foot = 7

90 - 27= 63

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Hello,

By comparison, let x = height of the object , y = height of the shadows,

x : y = 10 : 7

y = (7/10 ).x,

when x = 90,

y = (7/10) . 90 = 7 x 9 = 63 foots....

thanks...

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Archiet Dev
Apr 25, 2014

A simple-Ratio & Proportion question.

If 10 Foot tall Hoop cast 7 Foot Shadow.

Again,

Then,the shadow of 90 Foot Tall Hotel"s will be =10/7 :: 90/X

solving this equation will give- = (90 * 7) / 10 

                                                                                        = 630 / 10

                                                                                        = 63

So,The height of the shadow is.63m

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