Two squares of side x centimetre and
( x+4 cm). the sum of the areas is 656 square CM Express this as an algebraic equation in X and solve the equation to find the sides of the squares .
Answers
Answer:
Sides of square are of length 16 cm and 20 cm.
Step-by-step explanation:
From the properties of quadrilaterals :
- Area of square = a^2 , where a represents the side of that square.
Here,
Two squares of sides( x cm and x + 4 cm ) are given.
= > Area of square of side x cm = ( x cm )^2 { Since length of side of this square is x cm }
= > Area of square of side x cm = x^2 cm^2
= > Area of square of side x cm = ( x + 4 cm )^2 { Since length of side of this square is x + 4 cm }
= > Area of square of side x cm = ( x^2 + 4 + 8x )cm^2 { Using ( a + b )^2 = a^2 + b^2 + 2ab, ( x + 4 ) = x^2 + 16 + 8x }
Given,
Sum of area of both squares is 656 cm^2
= > Area of square of side x cm + area of square of side x + 4 cm = 656 cm^2
= > x^2 cm + x^2 cm + 16 cm^2 + 8x cm^2 = 656 cm^2
= > 2x^2 + 16 + 8x = 656
= > 2x^2 + 8x + 16 - 656 = 0
= > 2x^2 + 8x - 640 = 0
= > x^2 + 4x - 320 = 0
Required algebraic equation in terms of x to represent the situation is x^2 + 4x - 320 = 0
Solving further for the value of x :
= > x^2 + ( 20 - 16 )x - 320 = 0
= > x^2 + 20x - 16x - 320
= > x( x + 20 ) - 16( x + 20 ) = 0
= > ( x + 20 )( x - 16 ) = 0
Since their product is 0, one of them must be 0.
If x + 20 is 0 = > x + 20 = 0 = > x = - 20
If x - 16 is 0 = > x - 16 = 0 = > x = 16
Neglecting x = - 20 { since length can't be negative }
x = 16
Lengths of sides of squares are : 16 cm and 16 cm + 4 cm ( or 20 cm ).