The breadth of a rectangle is 7 cm less than its length and the diagonal is 1cm more than the length. Find the breadth of the rectangle.
Answers
Answer:
Length of rectangle=12 cm
Breadth of rectangle=5 cm
Step-by-step explanation:
Let length of rectangle=x
Breadth of rectangle=x-7
Diagonal of rectangle=x+1
(x+1)^2=x^2+(x-7)^2(x+1)
2
=x
2
+(x−7)
2
Using Pythagoras theorem
(Hypotenuse)^2=(Base)^2+(Perpendicular\;side)^2(Hypotenuse)
2
=(Base)
2
+(Perpendicularside)
2
x^2+1+2x=x^2+x^2-14x+49x
2
+1+2x=x
2
+x
2
−14x+49
Using identity:(a-b)^2=a^2+b^2-2ab(a−b)
2
=a
2
+b
2
−2ab
(a+b)^2=a^2+b^2+2ab(a+b)
2
=a
2
+b
2
+2ab
1=2x^2-x^2-14x+49-2x-x^21=2x
2
−x
2
−14x+49−2x−x
2
1-49=x^2-16x1−49=x
2
−16x
-48=x^2-16x−48=x
2
−16x
x^2-16x+48=0x
2
−16x+48=0
x^2-12x-4x+48=0x
2
−12x−4x+48=0
x(x-12)-4(x-12)=0x(x−12)−4(x−12)=0
(x-12)(x-4)=0(x−12)(x−4)=0
x-12=0\implies x=12x−12=0⟹x=12
x-4=0\implies x=4x−4=0⟹x=4
Length of rectangle=12 cm
Breadth of rectangle=12-7=5 cm
Diagonal of rectangle=12+1=13 cm
If Length of rectangle=4 cm
Breadth of rectangle=4-7=-3 cm
It is not possible because breadth cannot be negative.
Step-by-step explanation:
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