Question

A rectangle has an area of 35.60 cm^{2}. When both the
length and width of the rectangle are increased by 1.40 cm, the
area of the rectangle becomes 55.62 cm^{2}. Calculate the
length of the shorter of the two sides of the initial
rectangle.

Answer #1

Area of the rectangle = A = 35.6 cm^{2}

Length of the rectangle = L

Width of the rectangle = W

A = LW

LW = 35.6

The length and width of the rectangle are now increased by 1.4 cm each.

New area of the rectangle = A_{1} = 55.62
cm^{2}

New length of the rectangle = L_{1} = L + 1.4

New width of the rectangle = W_{1} = W + 1.4

A_{1} = L_{1}W_{1}

55.62 = (L + 1.4)(W + 1.4)

55.62 = LW + 1.4L + 1.4W + 1.96

55.62 = 35.6 + 1.96 + 1.4(L + W)

L + W = 12.9

L = 12.9 - W

LW = 35.6

(12.9 - W)W = 35.6

12.9W - W^{2} = 35.6

W^{2} - 12.9W + 35.6 = 0

W = 8.9 cm or 4 cm

L = 12.9 - W

Therefore if W is 8.9 cm then L is 4 cm or if W is 4 cm then L is 8.9 cm.

**Length of the shorter side = 4 cm**

A rectangle has an area of 30.26 cm2. When both the length and
width of the rectangle are increased by 1.80 cm, the area of the
rectangle becomes 55.64 cm2. Calculate the length of the shorter of
the two sides of the initial rectangle.

A rectangle has an area of 42.18 cm2. When both the length and
width of the rectangle are increased by 1.30 cm, the area of the
rectangle becomes 63.24 cm2. Calculate the length of the shorter of
the two sides of the initial rectangle.
The answer of 2.5 has been marked incorrect.

A rectangle has an area of 36.36 cm2. when both the length and
width of the rectangle are increased by 1.40cm, the area of the
rectangle becomes 57.50cm2. calculate the length of the tow sides
of the initial rectangle.

The length of a rectangle is increasing at a rate of 5 cm/s and
its width is increasing at a rate of 4 cm/s. When the length is 15
cm and the width is 6 cm, how fast is the area of the rectangle
increasing?

The length of a rectangle is increasing at a rate of 8 cm/s and
its width is increasing at a rate of 9 cm/s. When the length is 9
cm and the width is 5 cm, how fast is the area of the rectangle
increasing?

the length of a rectangle is 4 inches more than its width. the
area of the rectangle is equal to 5 inches more than 2 times the
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Results for Table Top
Length (cm)
Width (cm)
Thickness (cm)
Area (cm2)
Volume (cm3)
12.5
7.9
2.1
98.75
207.38
2. Estimate the error in
each of the measurements and calculate its % error.
Quantity
Length
Width
Thickness
Estimated Error
% Error
3. Use these results to
calculate the % error in the area and volume.
Quantity
Area
Volume
% Error

the
length of a rectangle is 3 ft less than twice the width. the area
of the rectangle is 27 ft^2. find the dimensions

Find the length and width of a rectangle that has the given
perimeter and a maximum area.
Perimeter: 316 meters

Find the length and width of a rectangle that has the given
perimeter and a maximum area.
Perimeter: 108 meters

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