Find the perimeter of a parallelogram whose base is 8cm and another side is12cm. Solve step by step please

step 1: draw a parallelogram slanting right and label the base 12 and the slant height 8.

step 2: draw a diagonal from top left to bottom right.

step 3: construct an altitude from the top left vertex down to the base. call that "h".

step 4: call the left side segment "a" and the right side segment "b". a + b = 12.

step 5: we have 2 pythagorean theorems: (i) a%5E2+%2B+h%5E2+=+8%5E2; (ii) b%5E2+%2B+h%5E2+=+10%5E2.

step 6: by subtracting the two, we get (iii) b%5E2+-+a%5E2+=+36.

step 7: find values for a and b such that (b+a)(b-a) = 36. If b= 9 and a = 3, we have the values.

By using either (i) or (ii), this also gives us the height, h, as sqrt(55).

step 8: draw the other diagonal. Since we are dealing with a parallelogram, opposite sides have the same slope. So, the base grows from 12 to 15.

step 9: we apply another pythagorean theorem to our new triangle. (iv) 15%5E2+%2B+sqrt%2855%29%5E2+=+d%5E2

step 10: solve for d. we get d^2 = 225 + 55 = 280. So, d ~ 16.7332.

Hope this helps :)

step-by-step explanation:

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b: |12 – x| ≤ 0.25

step-by-step explanation:      

let x be the possible lengths in inches, of the ribbons jaime cut.

we have been given that jaime is cutting strips of ribbon for a project. he tries to cut each piece to be 12 inches long, but sometimes he cuts it too long or too short by as much as 0.25 inch.  

we can represent this information in an inequality as:

by the definition of absolute value function we will get,

upon combining our inequalities we will get,

therefore, the inequality   describes all the possible lengths (x), in inches, of the ribbons jaime cut.

step-by-step explanation: