Question 252312: a parallelogram with sides 12cm,8cm with one of the diagonal 10cm,find the length of other diagonal? Answer by drk(1908) (Show Source):
You can put this solution on YOUR website! 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) ; (ii) .
step 6: by subtracting the two, we get (iii) .
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)
step 10: solve for d. we get d^2 = 225 + 55 = 280. So, d ~ 16.7332.
Hope that helps.
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