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The width of a rectangle is 4cm less than the length. If each dimension were increased by 3cm, the width of the new rectangle formed would b
Question
The width of a rectangle is 4cm less than the length. If each dimension were increased by 3cm, the width of the new rectangle formed would be 2/3 the length of the new rectangle. Find the dimensions of the original rectangle.
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Mathematics
3 years
2021-08-04T10:10:32+00:00
2021-08-04T10:10:32+00:00 1 Answers
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Answer:
The original length is 9 cm and the original width 5 cm
Step-by-step explanation:
The area of a rectangle A is given as the product of its’ length L and width W.
Given that the width of a rectangle is 4cm less than the length then
W = L – 4
If each dimension were increased by 3cm, then the new
Length
= L + 3
Width
= W + 3
the width of the new rectangle formed would be 2/3 the length of the new rectangle
W + 3 = 2/3(L + 3)
3W + 9 = 2L + 6
3W = 2L +6 – 9
3W = 2L – 3
Recall that W = L – 4
3(L – 4) = 2L – 3
3L – 12 = 2L – 3
3L – 2L = 12 – 3
L = 9 cm
W = 9 – 4
= 5 cm