Math

QuestionFind the other side length ww of a rectangle with area 25714257 \frac{1}{4} in² and one side 101210 \frac{1}{2} in.

Studdy Solution

STEP 1

Assumptions1. The area of the rectangle is 25714257 \frac{1}{4} square inches. One side length (let's call it ll) is 10110 \frac{1}{} inches3. We need to find the length of the other side (let's call it ww)
4. The area of a rectangle is calculated by multiplying the lengths of its two sides Area=l×wArea = l \times w

STEP 2

First, we need to express the mixed numbers as improper fractions to make the calculations easier.For l=1012l =10 \frac{1}{2}, we multiply the whole number part (10) by the denominator of the fractional part (2) and add the numerator of the fractional part (1). This gives us the numerator of the improper fraction. The denominator remains the same.
l=10×2+12l = \frac{10 \times2 +1}{2}

STEP 3

Calculate the value of ll.
l=10×2+12=212l = \frac{10 \times2 +1}{2} = \frac{21}{2}

STEP 4

Similarly, for the area Area=25714Area =257 \frac{1}{4}, we convert the mixed number to an improper fraction.
Area=257×4+14Area = \frac{257 \times4 +1}{4}

STEP 5

Calculate the value of the area.
Area=257×4+14=10294Area = \frac{257 \times4 +1}{4} = \frac{1029}{4}

STEP 6

Now that we have the area and one side length, we can find the length of the other side by rearranging the formula for the area of a rectangle.
w=Arealw = \frac{Area}{l}

STEP 7

Plug in the values for the area and ll to calculate ww.
w=1029/421/2w = \frac{1029/4}{21/2}

STEP 8

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
w = \frac{102/4}{21/2} = \frac{102/4} \times \frac{2/21}

STEP 9

Calculate the value of ww.
w=1029/4×2/21=514.5.5w = \frac{1029/4} \times \frac{2/21} = \frac{514.5}{.5}

STEP 10

implify the fraction to get the decimal value of ww.
w=514.510.5=49w = \frac{514.5}{10.5} =49So, the length of the other side of the rectangle is49 inches.

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