Question

FORMING AND SOLVING EQUATION

a) Rectangle a has one side which is 6cm long and the other is (x+2)cm long.Rectangle b has sides of length (2x+1) and 3cm. If the perimeters are the same, calculate the value x and hence, the lengths of the sides of the rectangles

b) Rectangle x measures 7cm by (x+1)cm. Rectangle y has dimensions of (3x+6)cm and 4cm. The area of rectangle x is half the area of rectangle y. calculate the lengths of the sides of the rectangles, and hence, their areas

c) Adam has sticks of the following lengths: (3x+4)cm (2x+10)cm (x+12)cm
he puts all 3 sticks together to make a triangle. the triangle is isosceles. calculate the 3 possible values of x



ALL WORKING OUT PLEASE

Answer 1

b and c

Explanation:

Answer 2

We know, Perimeter of a rectangle = 2(l + w)
2(6+x+2) = 2(3+2x+1)
2(8+x) = 2(4+2x)
16+2x = 8+4x
16-8 = 4x - 2x
8 = 2x
x = 4

Unknown lengths, x+2 = 4+2 = 6
2x+1 = 2(4)+1 = 8+1 = 9

2) We know, Area of a rectangle = a * b
2[7(x+1)] = 4(3x+6)
2[7x+7] = 12x+24
14x+14 = 12x+24
14x-12x = 24-14
2x = 10
x = 5

Lengths of unknown sides, x+1 = 5+1 = 6 cm
3x+6 = 3(5)+6 = 15+6 = 21 cm

Hope this helps!