The lengths of corresponding sides of two squares are in the ratio of 3:1. If the area of the larger square exceeds the area of the smaller square by 63 in.², find the area of the smaller square

The area of the smaller square is 7.875 square inches

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Remember that all the squares are similar

Let

z ----> the scale factor

x ---> the area of the larger square

y ---> the area of the smaller square

so

we have

---> scale factor

substitute

----> equation A

That means---> the area of the larger square is 9 times greater than the area of the smaller square

The area of the larger square exceeds the area of the smaller square by 63 in.²

so

----> equation B

Equate equation A and equation B

solve for y

therefore

The area of the smaller square is 7.875 square inches

the length of o'p' is .

step-by-step explanation:

it is given that the quadrilateral m'n'o'p' is the image of quadrilateral mnop after dilation.

the center of dilation is origin and the scale factor is 1.5.

in dilation the image and preimge are similar figures. it means the sides of image and preimage are proportional.

the scale factor is defined as

the scale factor is 1.5.

multiply both sides by op.

note: if the value of op is given, then multiply the value of op with 1.5 to get the length of side o'p'.

therefore length of o'p' is .

the aswere is the one with all 8's and the second one is with the 10,8 and 6

step-by-step explanation: