OK.
So you've solved part-a), and you know how far the roof sticks out past
the wall. Great work ! I'm proud of ya! You need to know that for part-b).
Do you see the little tiny right triangle up there, between the roof overhang
and the line for the winter sun ? You know the length of the roof overhang,
and the small acute angle at the tip of the roof is the same as the elevation
of the sun ... 28°. With that information, you can solve the little right triangle,
and find the length of the vertical leg, which is a small part of the house wall.
That little piece of the wall is in the shadow of the roof overhang,and the rest
of the roof is in direct sunlight. Subtract the little piece from 20-ft, and the rest
is the height of the part of the wall that's in direct sunlight.
5.
6 / t = 9 / (t+2)
9t = 6t + 12
3t = 12
t = 4 answer
The remaining length:-
6 / 4 = 11 / x
6x = 44 so x = 7.33 answer
6. 8 / w = 6 / (w - 5)
6w = 8w - 40
2w = 40 so w = 20 answer
The side marked w - 5 = 20-5 = 15 answer
8/14 = 20/x giving the top side = 35 answer
Answer:
a) a +b= 13, ab= 40
b) length= 8m, width= 5m
Step-by-step explanation:
Perimeter of rectangle= 2(length +width)
Area of rectangle= length ×width
a) Perimeter= 26m
2(a +b)= 26
Divide both sides by 2:
a +b= 26 ÷2
a +b= 13 ----- (1)
Area= 40m²
ab= 40 ----- (2)
b) From (1): a= 13 -b ----- (3)
Substitute (3) into (2):
(13 -b)(b)= 40
Expand:
13b -b²= 40
b² -13b +40= 0
Factorise:
(b -5)(b -8)= 0
b -5= 0 or b -8= 0
b= 5 or b= 8
Substitute into (3):
a= 13 -5 or a= 13 -8
a= 8 or a= 5
Since the length is usually the longer side of the rectangle, the length and the width of the rectangular garden is 8m and 5m respectively.