Determine the dimensions of a retangle with a perimeter of 30 cm and a width 5 cm less than its length.

Grace was asked to determine the demensions of a retangle with a perimeter of 30 cm and a width 5 cm lss than its length. Write and solve an equation to determine the dimensions of the rectangle.

also..

5 buckets of sand and 1/2 of another bucket are added together. The total mass is 4.4kg. How much sand does each bucket hold? Explain.

for the first one the total perim is 30.

We know that the width is 5 less than its length.

So the width is l-5.

and its length is l. So the perimieter is just the 4 sides added up therefore;

l-5 + l-5 + l+l=30 (total perimeter)

4l -10 = 30

4l = 40

l = 40/4 = 10

so l =10

w=l-5

w=10-5

w=5cm
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for ur second one

we know that 5x + 1/2x = 4.4

so 5.5 x =4.4

x = 0.8

each bucket can hold 0.8 kg

2x+( 2x -10)=30
30+10=40 so
2x +2x =4x
4x = 40
x =10

I dunno i haven't done algebra in years and i never want to have to-my brain is fried trying to do one question!!!!

4.4 divided by 5.5= 0.8 which means that there is 800g in each bucket and 400g inthe 1/2 bucket!


from polly♥

1. let length =x then width=(x-5)
perimeter = 2lengths +2widths
so 2x+2(x-5)=30
4x-10=30 giving x=10 so the dimensions =10cm by 5cm

2. let each bucket hold x kg
5x +x/2 = 4.4 ie 11x/2 =4.4 so 11x=8.8 giving x=0.8

w=l-5
p=2w+2l
p=2(l-5)+2l=30
4l-10=30
4l=40
l=10cm

w=l-5
w=10-5
w=5cm

A=w*l=5*10=50cm^2


5.5b=4.4
b=4.4/5.5
b=4*1.1/(5*1.1)
b=4/5kg=0.8kg