# 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 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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Approved by eNotes Editorial Team

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