diagonal of the rectangle shown in the figure is 13 centimeters and it's area 60 square centimeters . Taking the length of sides are x centimeters and y centimeters . (a) what the number are xy and x²+y²?. (b) Find the number x+y and x-y?. (c) Find the sides of the rectangle.?
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Step-by-step explanation:
Given Diagonal of the rectangle shown in the figure is 13 centimeters and it's area 60 square centimeters . Taking the length of sides are x centimeters and y centimeters . (a) what the number are xy and x²+y²?. (b) Find the number x+y and x-y?
- Given diagonal d = 13 cm and Area of rectangle a = 60 sq cm
- Now Area of a rectangle = length x breadth
- So length = x cm and breadth = y cm
- Area of the rectangle = x x y
- 60 = xy
- xy = 60
- So d^2 = x^2 + y^2
- Or x^2 + y^2 = 13^2
- Or x^2 + y^2 = 169
- Or xy = 60
- Now (x + y)^2 – 2xy = 169
- (x + y)^2 = 169 + 2xy
- (x + y)^2 = 169 + 2(60)
- (x + y)^2 = 169 + 120
- = 289
- Or (x + y) = 17
- Now (x – y)^2 = x^2 + y^2 – 2xy
- = 169 – 2(60)
- = 169 – 120
- = 49
- Or x – y = 7
- Now x + y = 17
- x – y = 7
- So 2x = 24
- Or x = 12 cm
- So x – y = 7
- 12 – y = 7
- 12 – 7 = y
- Or y = 5 cm
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https://brainly.in/question/12104237
Answered by
3
Step-by-step explanation:
Xy=60
(X+Y)=17
X-Y=7
X=12cm
Y=5cm
Hope it helps you
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