Mathematics, 19.05.2020 23:49, angellll4455

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

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answered: Brittpaulina

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 :)

answered: Guest

the system of inequity is

$y\leq -x+4$

$3y> x$

step-by-step explanation:

from the given graph it is noticed that we have two related lines. one is solid and another is dashed.

if a line passing through two points, then the equation of line is

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

the solid line passing through the points (0,4) and (4,0).

$y-4=\frac{0-4}{4-0}(x-0)$

$y=-x+4$

the related equation of solid line is $y=-x+4$ .

similarly, find the related equation of dashed line. the dashed liune passing through the points (0,0) and (3,1).

$y-0=\frac{0-1}{3-0}(x-0)$

$3y=x$

the related equation of dashed line is $3y=x$

from the given graph it is noticed that the point (0,1) lies on the shaded region, therefore the point (0,1) must be satisfied by the related equations.

check the related equations by the point (0,1).

$1=-0+4$

$1=4$

this statement is true if the sign of inequality is < instead of equality. since it is an solid line therefore the sign of inequality will be $\leq$ . the required inequality is