SOLUTION: 1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle. 2)A lidles box is constructed from a square piece of tin by cutting a 10cm s

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Question 394674: 1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle.
2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre.
Answer by jrfrunner(365) About Me  (Show Source):
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1)The hypothenuse of right triangle is 15cm. the sum of the legs is 21cm. Find the legs of triangle.
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Given: c=15, a+b=21
thus a=21-b
Pythagoream theorem: c^2=a^2+b^2
15%5E2=%2821-b%29%5E2%2Bb%5E2
15%5E2=21%5E2-42b%2Bb%5E2%2Bb%5E2
0=2b%5E2-42b%2B216
0=b%5E2-21b%2B108
b=18/2=9 or b=24/2=12
Thus the legs of the triangle are a=21-b=21-9=12, b=9,c=15
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2)A lidles box is constructed from a square piece of tin by cutting a 10cm square from each corner and bending up the sides for the box. if the volume of the box is 1200cm^3,find the dimensions to the nearest tenth of centimetre
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The base of the box will be square and measure x-2*(10)=x-20
The volume of the box: length*width*height= (x-20)*(x-20)*10=1200
therefore
(x-20)^2=120
x^2-40x+400=120
x^2-40x+280=0
use the quadratic formula
x=(40-21.9)/2=9.05 or x=(40+21.9)/2=30.95
since the base has dimensions x-20 and x-20, x has to be greater than 20
so x=9.05 cannot be one of the answers.
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Dimensions of the box length*width*height=30.95-20, 30.95-20,10
or 10.95,10.95,10