Advertisements
Advertisements
Question
Two squares have sides x cm and (x + 4) cm. The sum of their area is 656 sq. cm. Express this as an algebraic equation in x and solve the equation to find the sides of the squares.
Solution
Given that, two squares have sides x cm and (x + 4) cm.
Sum of their area = 656 cm2
∴ x2 + (x + 4)2 = 656
x2 + x2 + 16 + 8x = 656
2x2 + 8x – 640 = 0
x2 + 4x – 320 = 0
x2 + 20x – 16x – 320 = 0
x(x + 20) – 16(x + 20) = 0
(x + 20)(x – 16) = 0
x = –20, 16
But, x being side, cannot be negative.
So, x = 16
Thus, the sides of the two squares are 16 cm and 20 cm.
APPEARS IN
RELATED QUESTIONS
The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.
The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:
- the value of x,
- the lengths of its sides,
- its area.
The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.
The perimeter of a rectangle is 104 m and its area is 640 m2. Find its length and breadth.
A footpath of uniform width runs round the inside of a rectangular field 32 m long and 24 m wide. If the path occupies 208 m2, find the width of the footpath.
The dimensions of a rectangular field are 50 m and 40 m. A flower bed is prepared inside this field leaving a gravel path of uniform width all around the flower bed. The total cost of laying the flower bed and gravelling the path at Rs. 30 and Rs. 20 per square metre, respectively, is Rs. 52,000. Find the width of the gravel path.
The area of a big rectangular room is 300 m2. If the length were decreased by 5 m and the breadth increased by 5 m; the area would be unaltered. Find the length of the room.
A car made a run of 390 km in ‘x’ hours. If the speed had been 4 km/hour more, it would have taken 2 hours less for the journey. Find ‘x’.
In the given figure, the value of x is ______.
The length of a rectangle is 3 m more than its width. If its area is 180 m2; the length of the rectangle is ______.
