Mr. Moses has a rectangular garden with an area of 1 9 2 m 2 . The difference between the length and width is 4 m . Along the sides and within the garden, he paved a road of width 2 meters. Find the area of the road in m 2 .
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Assume that p = length and l = width
We already know that p − l = 4
Now let's find l
p × l = 1 9 2
( 4 + l ) × l = 1 9 2
4 l + l 2 = 1 9 2
l 2 + 4 l − 1 9 2 = 0
( l − 1 2 ) ( l + 1 6 ) = 0
l = 1 2
p = 4 + l = 4 + 1 2 = 1 6
Now find the area of the road
4 road square shaped area located in the garden corners with a side length of 2 m
4 × 2 2 = 1 6 m 2
2 road area that are in the garden length with side length 1 2 m and width 2 m
2 × ( 1 2 m × 2 m ) = 4 8 m 2
2 road area that are in the garden width with side length 8 m and width 2 m
2 × ( 8 m × 2 m ) = 3 2 m 2
So the area of the road is 1 6 m 2 + 4 8 m 2 + 3 2 m 2 = 9 6 m 2
M a t h i s m o r e e n j o y a b l e t h a n t h e g a r d e n p i c t u r e ! ! !
Sorry I got confused. You calculated the garden to be 12 m x 16 m. Then why are you taking 'side length 8 m'? Should it not be 16? I got the answer as 1 2 × 2 × 2 + 1 6 × 2 × 2 + 2 × 2 × 4 = 1 2 8 What am I missing?
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8 comes from 1 2 − 2 − 2 , i suggest you to draw the garden rather than imagine it, you'll understand it after you draw it
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Ok, so this road is running 'inside' the 12 x 16 rectangle?
So another wording problem. And thankfully I am not the only one. Be clear that you are paving garden on the inside, and not expanding it out.
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Let the garden area =W *L=W(W+4)=192=12 *(12+4).
So W=12, L=16.
Area of road =2 *{W *2+(L-2 *2)}=2{24+24}= 9 6 .