Mathematics, 18.11.2020 01:20 Alexaisokay1

Please help: If the area of a rectangular picture of a stamp is 81 times greater than the actual stamp's area, and the stamp has a length of 4/3". what is the length of the stamp's picture? I know the answer is 12 inches but not sure how to get there so pls explain

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Answer from: moonk7733

12 inches.

Step-by-step explanation:

We know that the length of the stamp is 4/3 inches.

Let the width be x inches.

Then the area of the actual stamp is:

$\frac{4}{3}x\text{ inches}^2$

We know that the rectangular picture of the stamp is 81 times greater than the actual stamp’s area. Therefore, the area of the picture is 81 times the above. So:

$81(\frac{4}{3}x)\text{ inches}^2$

So, the area of the rectangular picture is the area of the actual stamp multiplied by a scale factor k.

When we use the scale factor to scale area, we need to square it. Hence, the area of the actual stamp times the scale factor squared is equal to the area of the rectangular picture. Therefore:

$\frac{4}{3}x(k^2)=81(\frac{4}{3}x)$

Let’s solve for the scale factor. Divide both sides by 4/3(x). Hence:

k^2=81

Take the square root of both sides:

k=9

So, the scale factor from the actual stamp to the picture is 9.

So, the actual stamp has a length of 4/3.

Then ThThe length of the stamp’s picture will be:

$\frac{4}{3}k$

Substitute 9 in for k to get:

$=\frac{4}{3}(9)=12$

So, the length of the stamp’s picture is 12 inches.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

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