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If the length of a rectangle is increased by 8 m and its width by 3 m, its area will be increased by 200 sq.m. If its length is increased by 3 m and its width by 8 m, its area will be increased by 255 sq.m. What are the original dimensions of the rectangle?

Sagot :

AGBOIIIN

Answer:

  • length = 24 meters
  • width = 13 meters

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ANONYMOUSBETAIN

In the formula of the rectangle , we know that

y=xz

where x and z are the sides and y is the area

For the first statement , our formula will be

(x+8)(z+3) = y + 200

Next is we simplify it

xz + 3x + 8z + 24 = y + 200

Now substitute some values

3x + 8z = y - y + 200 - 24

3x + 8z = 176

for the second one, it will be

(x+3)(z+8) = y + 255

Simplify

xz +8x + 3z + 24 = y + 255

substitite

8x + 3z = y - y + 255 - 24

8x + 3z = 231

Next is we do some elimination

(-8/3)(3x + 8z = 176)

8x + 3z = 231

-8x - 64z/3 = -1408/3

(-3/55)(-55z/3 = -1408/3 + 693/3)

z = 13

Next is find for x

8x + 3(13) = 231

(1/8)(8x = 231 - 39)

x = 24

Answer

24m and 13m

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