ABCD is an isosceles trapezoid with legs AB and CD. And with Base BC. If AB = 6z - 5 and BC = 7z + 4 and. CD = 4z + 3.
A.
Sketch:
Identify the shorter side and longer side.
B.
Find z.
work:
C.
Find BC.
work:
A. Sketch:
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A ------------- B
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D ------------- C
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In the isosceles trapezoid ABCD, legs AB and CD are equal in length, and base BC is longer than AB and CD.
The shorter side is AB, while the longer side is BC.
B. Find z.
In an isosceles trapezoid, the diagonals are equal in length. So, we have:
AB + CD = BC
Substituting the given values, we get:
6z - 5 + 4z + 3 = 7z + 4
Solving for z, we get:
z = 6
C. Find BC.
Using the given value of z, we have:
BC = 7z + 4 = 7(6) + 4 = 46
Therefore, BC = 46.
A. To sketch the isosceles trapezoid ABCD, draw a horizontal line for the base BC. Label the endpoints as B and C. From point B, draw a slanted line upwards and label the endpoint as A. From point C, draw a slanted line downwards and label the endpoint as D.
The shorter side of the trapezoid is AB, while the longer side is CD.
B. To find the value of z, we need to equate the measures of the legs AB and CD. In an isosceles trapezoid, the legs are congruent.
AB = CD
Given that AB is 6z - 5 and CD is 4z + 3, we can set up the equation:
6z - 5 = 4z + 3
Simplifying the equation:
6z - 4z = 3 + 5
2z = 8
z = 4
Therefore, z = 4.
C. To find the measure of BC, we can substitute the value of z into the given expression for BC:
BC = 7z + 4
Substituting z = 4:
BC = 7(4) + 4
BC = 28 + 4
BC = 32
Therefore, BC is equal to 32.
A. Sketch:
To sketch the isosceles trapezoid ABCD, draw a trapezoid shape with parallel sides AB and CD. Label the bases as BC and AD.
The shorter side of the trapezoid is AB, and the longer side is CD.
B. Find z.
To find z, set the lengths of the legs equal to each other:
AB = CD
Therefore, 6z - 5 = 4z + 3.
Solve for z:
6z - 4z = 3 + 5
2z = 8
z = 4
So, z is equal to 4.
C. Find BC.
To find BC, substitute the value of z into the expression for BC:
BC = 7z + 4
BC = 7(4) + 4
BC = 28 + 4
BC = 32
Therefore, BC is equal to 32.