the sum of the length, width,and height of a rectangle box is 75cm. The length is twice the sum of the width and height, and twice the width exceeds the height by 5cm. Find the dimensions of the box

Expert Answers

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Let l be the length, h the height and w the width of the box.

(1)l+w+h=75 Sum of lengthwidth and height is 75

(2)l=2(w+h) Length is twice the sum of width and height

(3)2w=h+5 Twice the width is 5 more than the height

From (3) we get h=2w-5

Substituting into (2) we get l=2(w+2w-5) or l=6w-10

Substituting into (1) we get:

6w-10+w+2w-5=75

9w-15=75

9w=90

w=10

Then h=2(10)-5=15 and l=6(10)-10=50

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The length is 50cm, the width is 10cm, and the height is 15cm

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