# Percent change

If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?

Correct result:

p =  12.5 %

#### Solution:

$q_{1}=1+25/100=\dfrac{ 5 }{ 4 }=1.25 \ \\ q_{2}=1-10/100=\dfrac{ 9 }{ 10 }=0.9 \ \\ \ \\ S_{1}=ab \ \\ S_{2}=(a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) \ \\ \ \\ p=100 \cdot \ \dfrac{ S_{2}-S_{1} }{ S_{1} } \ \\ \ \\ p=100 \cdot \ \dfrac{ (a \cdot \ q_{1}) \cdot \ (b \cdot \ q_{2}) - ab }{ ab } \ \\ \ \\ p=100 \cdot \ \dfrac{ q_{1} \cdot \ q_{2}-1 }{ 1 }=100 \cdot \ \dfrac{ 1.25 \cdot \ 0.9-1 }{ 1 }=\dfrac{ 25 }{ 2 }=12.5 \%$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Tips to related online calculators

#### You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

## Next similar math problems:

• Part-time workers
Three part-time workers received CZK 1,235 for their work. The first received 20% less than the second and the third received 45 CZK more than the second. Determine how many crowns (CZK) each of them received.
• Solutions, mixtures
We have 2 liters of 20% solution available. How much 70% solution do we need to add to it to get a 30% solution?
• Diagonal BD
Find the length of the diagonal BD in a rectangular trapezoid ABCD with a right angle at vertex A when/AD / = 8,1 cm and the angle DBA is 42°
• Truncated cone 6
Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.
• The regular
The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• Hexagonal pyramid
Find the area of a shell of the regular hexagonal pyramid, if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm.
• Sow barley
Farmers wanted to sow barley within 13 days. Due to the excellent weather, they managed to exceed the daily plan of sowing by 2 ha and therefore finished sow grain in 12 days. How many hectares of land did they sow with barley?
• Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
• Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
• Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body.
• Big numbers
How many natural numbers less than 10 to the sixth can be written in numbers: a) 9.8.7 b) 9.8.0
• Company car
Ms. Vaňková has a company car equipped with a multifunction indicator, on which she can monitor the average petrol consumption during individual rides. During the first ride, mostly in city traffic, it traveled 20.5 km, with an average consumption of 7.8L
• Parallelogram
Find the perimeter of the parallelogram, where base a = 8 cm, height v = 3 cm, and angle alpha = 35° is the magnitude of the angle at vertex A.