Q:
The sum of the areas of two squares is 818 cm².
The sum of the perimeters is 160 cm.
Find the lengths of the sides of the squares.
I don't want the answer please help me to make it a equation its a simultaneous equation question
Answers
Step-by-step explanation:
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Therefore the length of of sides of the squares are 17 cm and 23 cm.
Step-by-step explanation:
Let the length of sides of the squares be a and b.
The area of a square = side²
Therefore the area of the first square is a² cm²
Therefore the area of the second square is b² cm².
The perimeter of a square = 4×side
The perimeter of the first square = 4a cm
The perimeter of the second square = 4b cm
According to the problem,
4a+4b=160
⇒4(a+b)=160
⇒a+b=40 .........(1)
Again,
a²+b²=818
⇒(a+b)²-2ab=818 [ applying the formula x²+y²=(x+y)²-2xy]
⇒(40)²-2ab=818
⇒1600 -2ab =818
⇒ -2ab = 818-1600
⇒-2ab = -782
⇒ab = 391
391 = 17×23
17 and 23 are prime number.Only 17 and 23 are two factor of 391.
Therefore a =17 cm and b=23 cm
Therefore the length of of sides of the squares are 17 cm and 23 cm.